Properties

Label 77.a
Number of curves $1$
Conductor $77$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 77.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
77.a1 77a1 \([0, 0, 1, 2, 0]\) \(884736/539\) \(-539\) \([]\) \(4\) \(-0.78665\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 77.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 77.a do not have complex multiplication.

Modular form 77.2.a.a

sage: E.q_eigenform(10)
 
\(q - 3 q^{3} - 2 q^{4} - q^{5} - q^{7} + 6 q^{9} - q^{11} + 6 q^{12} - 4 q^{13} + 3 q^{15} + 4 q^{16} + 2 q^{17} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display