Properties

Label 3120.r
Number of curves $4$
Conductor $3120$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 3120.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3120.r1 3120g3 \([0, 1, 0, -7696, -261820]\) \(49235161015876/137109375\) \(140400000000\) \([2]\) \(3072\) \(1.0115\)  
3120.r2 3120g4 \([0, 1, 0, -7176, 230724]\) \(39914580075556/172718325\) \(176863564800\) \([4]\) \(3072\) \(1.0115\)  
3120.r3 3120g2 \([0, 1, 0, -676, -676]\) \(133649126224/77000625\) \(19712160000\) \([2, 2]\) \(1536\) \(0.66494\)  
3120.r4 3120g1 \([0, 1, 0, 169, 0]\) \(33165879296/19278675\) \(-308458800\) \([2]\) \(768\) \(0.31837\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 3120.r have rank \(1\).

Complex multiplication

The elliptic curves in class 3120.r do not have complex multiplication.

Modular form 3120.2.a.r

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} + q^{9} + q^{13} - q^{15} - 6 q^{17} - 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.