Properties

Label 77616em
Number of curves $1$
Conductor $77616$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("em1")
 
E.isogeny_class()
 

Elliptic curves in class 77616em

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
77616.v1 77616em1 \([0, 0, 0, -34359339, 80364797786]\) \(-260607143968297/11270993184\) \(-194014408274931072761856\) \([]\) \(11289600\) \(3.2342\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 77616em1 has rank \(1\).

Complex multiplication

The elliptic curves in class 77616em do not have complex multiplication.

Modular form 77616.2.a.em

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