Properties

Label 31713g
Number of curves $1$
Conductor $31713$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 31713g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
31713.f1 31713g1 \([0, 1, 1, 615681, 221020808]\) \(31490048/43923\) \(-36000533249057722323\) \([]\) \(662160\) \(2.4382\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 31713g1 has rank \(0\).

Complex multiplication

The elliptic curves in class 31713g do not have complex multiplication.

Modular form 31713.2.a.g

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{4} - 2 q^{5} + q^{9} + q^{11} - 2 q^{12} - q^{13} - 2 q^{15} + 4 q^{16} - 8 q^{17} + q^{19} + O(q^{20})\) Copy content Toggle raw display