Properties

Label 318402cg
Number of curves $2$
Conductor $318402$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("cg1")
 
E.isogeny_class()
 

Elliptic curves in class 318402cg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
318402.cg2 318402cg1 \([1, -1, 0, 23217, 93143917]\) \(189/512\) \(-3749209000722630144\) \([]\) \(7185024\) \(2.2430\) \(\Gamma_0(N)\)-optimal
318402.cg1 318402cg2 \([1, -1, 0, -14835543, 21999909077]\) \(-67645179/8\) \(-42705833773856208984\) \([]\) \(21555072\) \(2.7923\)  

Rank

sage: E.rank()
 

The elliptic curves in class 318402cg have rank \(0\).

Complex multiplication

The elliptic curves in class 318402cg do not have complex multiplication.

Modular form 318402.2.a.cg

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