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Properties

Label 381938.ca
Number of curves $2$
Conductor $381938$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("ca1")
 
E.isogeny_class()
 

Elliptic curves in class 381938.ca

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
381938.ca1 381938ca2 \([1, 1, 1, -41342, -3253253]\) \(-313994137/64\) \(-1592785347136\) \([]\) \(1710720\) \(1.3389\)  
381938.ca2 381938ca1 \([1, 1, 1, 173, -15083]\) \(23/4\) \(-99549084196\) \([]\) \(570240\) \(0.78959\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 381938.ca have rank \(0\).

Complex multiplication

The elliptic curves in class 381938.ca do not have complex multiplication.

Modular form 381938.2.a.ca

sage: E.q_eigenform(10)
 
\(q + q^{2} + 2 q^{3} + q^{4} - 3 q^{5} + 2 q^{6} - 2 q^{7} + q^{8} + q^{9} - 3 q^{10} - 6 q^{11} + 2 q^{12} + q^{13} - 2 q^{14} - 6 q^{15} + q^{16} - 6 q^{17} + q^{18} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.