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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)
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.