Properties

Label 311696b
Number of curves $1$
Conductor $311696$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 311696b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
311696.b1 311696b1 \([0, 0, 0, -1018699, 401518777]\) \(-4124632486295808/70140333767\) \(-1988126077257604592\) \([]\) \(7526400\) \(2.3097\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 311696b1 has rank \(1\).

Complex multiplication

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

Modular form 311696.2.a.b

sage: E.q_eigenform(10)
 
\(q - 3 q^{3} + 2 q^{5} - q^{7} + 6 q^{9} + q^{13} - 6 q^{15} + 2 q^{19} + O(q^{20})\) Copy content Toggle raw display