Properties

Label 311696.bi
Number of curves $1$
Conductor $311696$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("bi1")
 
E.isogeny_class()
 

Elliptic curves in class 311696.bi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
311696.bi1 311696bi1 \([0, 0, 0, -1067, -21670]\) \(-271063881/252448\) \(-125117267968\) \([]\) \(414720\) \(0.82590\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 311696.bi1 has rank \(1\).

Complex multiplication

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

Modular form 311696.2.a.bi

sage: E.q_eigenform(10)
 
\(q - 4 q^{5} - q^{7} - 3 q^{9} - 5 q^{13} + 6 q^{17} + q^{19} + O(q^{20})\) Copy content Toggle raw display