Properties

Label 1078.g
Number of curves $1$
Conductor $1078$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 1078.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1078.g1 1078k1 \([1, -1, 1, -6, -3]\) \(415233/88\) \(4312\) \([]\) \(144\) \(-0.58804\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1078.g1 has rank \(1\).

Complex multiplication

The elliptic curves in class 1078.g do not have complex multiplication.

Modular form 1078.2.a.g

sage: E.q_eigenform(10)
 
\(q + q^{2} - 3 q^{3} + q^{4} - 2 q^{5} - 3 q^{6} + q^{8} + 6 q^{9} - 2 q^{10} - q^{11} - 3 q^{12} + 7 q^{13} + 6 q^{15} + q^{16} - 2 q^{17} + 6 q^{18} + O(q^{20})\) Copy content Toggle raw display