Properties

Label 62790.v
Number of curves $8$
Conductor $62790$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("v1")
 
E.isogeny_class()
 

Elliptic curves in class 62790.v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
62790.v1 62790w7 \([1, 0, 1, -498774543, -4287535531454]\) \(13722604572968640187892492722921/36939806611960382108160\) \(36939806611960382108160\) \([2]\) \(19906560\) \(3.5646\)  
62790.v2 62790w8 \([1, 0, 1, -88636943, 237190054466]\) \(77013704252633562960444236521/20262661472595628847255040\) \(20262661472595628847255040\) \([2]\) \(19906560\) \(3.5646\)  
62790.v3 62790w5 \([1, 0, 1, -82029368, 285951093806]\) \(61042428203425827148268361721/2287149206968899000\) \(2287149206968899000\) \([6]\) \(6635520\) \(3.0153\)  
62790.v4 62790w6 \([1, 0, 1, -31561743, -65240015294]\) \(3477015524751011858387583721/173605868128473455001600\) \(173605868128473455001600\) \([2, 2]\) \(9953280\) \(3.2181\)  
62790.v5 62790w4 \([1, 0, 1, -8239368, -1567338194]\) \(61859347930211625693801721/34737934177406743101000\) \(34737934177406743101000\) \([6]\) \(6635520\) \(3.0153\)  
62790.v6 62790w2 \([1, 0, 1, -5134368, 4453877806]\) \(14968716721822395621081721/91209357028881000000\) \(91209357028881000000\) \([2, 6]\) \(3317760\) \(2.6688\)  
62790.v7 62790w1 \([1, 0, 1, -134368, 149877806]\) \(-268291321601301081721/9550359000000000000\) \(-9550359000000000000\) \([6]\) \(1658880\) \(2.3222\) \(\Gamma_0(N)\)-optimal
62790.v8 62790w3 \([1, 0, 1, 1206257, -3990069694]\) \(194108149567956675968279/6990401110687088640000\) \(-6990401110687088640000\) \([2]\) \(4976640\) \(2.8715\)  

Rank

sage: E.rank()
 

The elliptic curves in class 62790.v have rank \(1\).

Complex multiplication

The elliptic curves in class 62790.v do not have complex multiplication.

Modular form 62790.2.a.v

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} + q^{7} - q^{8} + q^{9} - q^{10} + q^{12} + q^{13} - q^{14} + q^{15} + q^{16} + 6 q^{17} - q^{18} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rrrrrrrr} 1 & 4 & 12 & 2 & 3 & 6 & 12 & 4 \\ 4 & 1 & 3 & 2 & 12 & 6 & 12 & 4 \\ 12 & 3 & 1 & 6 & 4 & 2 & 4 & 12 \\ 2 & 2 & 6 & 1 & 6 & 3 & 6 & 2 \\ 3 & 12 & 4 & 6 & 1 & 2 & 4 & 12 \\ 6 & 6 & 2 & 3 & 2 & 1 & 2 & 6 \\ 12 & 12 & 4 & 6 & 4 & 2 & 1 & 3 \\ 4 & 4 & 12 & 2 & 12 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.