Properties

Label 1290c
Number of curves $1$
Conductor $1290$
CM no
Rank $0$

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Show commands for: SageMath
sage: E = EllipticCurve("c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1290c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1290.d1 1290c1 \([1, 0, 1, 5066, -4779064]\) \(14382768678616871/9876709319915520\) \(-9876709319915520\) \([]\) \(10560\) \(1.7481\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1290c1 has rank \(0\).

Complex multiplication

The elliptic curves in class 1290c do not have complex multiplication.

Modular form 1290.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} + q^{7} - q^{8} + q^{9} + q^{10} + q^{12} + 7q^{13} - q^{14} - q^{15} + q^{16} - 4q^{17} - q^{18} + q^{19} + O(q^{20})\)  Toggle raw display