Properties

Label 40425ca
Number of curves $2$
Conductor $40425$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("ca1")
 
E.isogeny_class()
 

Elliptic curves in class 40425ca

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
40425.bt1 40425ca1 \([0, 1, 1, -1143, -15991]\) \(-56197120/3267\) \(-9608982075\) \([]\) \(27216\) \(0.67174\) \(\Gamma_0(N)\)-optimal
40425.bt2 40425ca2 \([0, 1, 1, 6207, -25546]\) \(8990228480/5314683\) \(-15631678506675\) \([]\) \(81648\) \(1.2211\)  

Rank

sage: E.rank()
 

The elliptic curves in class 40425ca have rank \(1\).

Complex multiplication

The elliptic curves in class 40425ca do not have complex multiplication.

Modular form 40425.2.a.ca

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{4} + q^{9} - q^{11} - 2 q^{12} - q^{13} + 4 q^{16} - 6 q^{17} + 7 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.