Properties

Label 248256.z
Number of curves $1$
Conductor $248256$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("z1")
 
E.isogeny_class()
 

Elliptic curves in class 248256.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
248256.z1 248256z1 \([0, 0, 0, -2265996, 1312915696]\) \(-6733388587405537/331008\) \(-63256613879808\) \([]\) \(3244032\) \(2.1237\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 248256.z1 has rank \(1\).

Complex multiplication

The elliptic curves in class 248256.z do not have complex multiplication.

Modular form 248256.2.a.z

sage: E.q_eigenform(10)
 
\(q - 2 q^{5} + 3 q^{7} + q^{11} - 2 q^{13} - 6 q^{17} + 8 q^{19} + O(q^{20})\) Copy content Toggle raw display