Properties

Label 85680ex
Number of curves $1$
Conductor $85680$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("ex1")
 
E.isogeny_class()
 

Elliptic curves in class 85680ex

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
85680.ea1 85680ex1 \([0, 0, 0, -685418592, 6908004458224]\) \(-11926249134908509075308544/2246680441062421875\) \(-6708551850125334720000000\) \([]\) \(24192000\) \(3.7653\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 85680ex1 has rank \(0\).

Complex multiplication

The elliptic curves in class 85680ex do not have complex multiplication.

Modular form 85680.2.a.ex

sage: E.q_eigenform(10)
 
\(q + q^{5} - q^{7} + 2 q^{11} - 5 q^{13} - q^{17} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display