Properties

Label 1078.f
Number of curves $1$
Conductor $1078$
CM no
Rank $0$

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Show commands: SageMath
sage: E = EllipticCurve("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1078.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1078.f1 1078e1 \([1, -1, 0, -625, 6173]\) \(551516475321/5632\) \(275968\) \([]\) \(864\) \(0.20221\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1078.f1 has rank \(0\).

Complex multiplication

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

Modular form 1078.2.a.f

sage: E.q_eigenform(10)
 
\(q - q^{2} + 3 q^{3} + q^{4} + 4 q^{5} - 3 q^{6} - q^{8} + 6 q^{9} - 4 q^{10} - q^{11} + 3 q^{12} + q^{13} + 12 q^{15} + q^{16} - 2 q^{17} - 6 q^{18} - 6 q^{19} + O(q^{20})\)  Toggle raw display