Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1290h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1290.f1 1290h1 \([1, 0, 1, 120229952, -3351306510322]\) \(192203697666261893287480365959/4963160303408775168000000000\) \(-4963160303408775168000000000\) \([]\) \(1068480\) \(3.9945\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1290h1 has rank \(0\).

Complex multiplication

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

Modular form 1290.2.a.h

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} - 3q^{7} - q^{8} + q^{9} - q^{10} + 4q^{11} + q^{12} - 3q^{13} + 3q^{14} + q^{15} + q^{16} - q^{18} + 7q^{19} + O(q^{20})\)  Toggle raw display