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Properties

Label 372810cv
Number of curves $2$
Conductor $372810$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("cv1")
 
E.isogeny_class()
 

Elliptic curves in class 372810cv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
372810.cv2 372810cv1 \([1, 0, 0, -2963990, -2036967900]\) \(-119305480789133569/5200091136000\) \(-125517558601488384000\) \([2]\) \(24837120\) \(2.6220\) \(\Gamma_0(N)\)-optimal
372810.cv1 372810cv2 \([1, 0, 0, -47909270, -127641047388]\) \(503835593418244309249/898614000000\) \(21690357429366000000\) \([2]\) \(49674240\) \(2.9686\)  

Rank

sage: E.rank()
 

The elliptic curves in class 372810cv have rank \(0\).

Complex multiplication

The elliptic curves in class 372810cv do not have complex multiplication.

Modular form 372810.2.a.cv

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} + 4 q^{7} + q^{8} + q^{9} + q^{10} + 4 q^{11} + q^{12} + 4 q^{13} + 4 q^{14} + q^{15} + q^{16} + q^{18} + 4 q^{19} + O(q^{20})\) 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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.