Properties

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

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

Elliptic curves in class 1078.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1078.a1 1078b1 \([1, -1, 0, -30634, -2056076]\) \(551516475321/5632\) \(32467359232\) \([]\) \(6048\) \(1.1752\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1078.a1 has rank \(1\).

Complex multiplication

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

Modular form 1078.2.a.a

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