Properties

Label 311696z
Number of curves $1$
Conductor $311696$
CM no
Rank $2$

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

Elliptic curves in class 311696z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
311696.z1 311696z1 \([0, -1, 0, -1335880, -573886432]\) \(109192361324/4173281\) \(10076547376992431104\) \([]\) \(4257792\) \(2.4144\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 311696z1 has rank \(2\).

Complex multiplication

The elliptic curves in class 311696z do not have complex multiplication.

Modular form 311696.2.a.z

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} - q^{7} - 2 q^{9} - q^{13} - q^{15} + 2 q^{17} - q^{19} + O(q^{20})\) Copy content Toggle raw display