Properties

Label 1290.l
Number of curves $1$
Conductor $1290$
CM no
Rank $1$

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Show commands for: SageMath
sage: E = EllipticCurve("l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1290.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1290.l1 1290l1 \([1, 1, 1, -45, 195]\) \(-10091699281/13932000\) \(-13932000\) \([]\) \(480\) \(0.063256\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1290.l1 has rank \(1\).

Complex multiplication

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

Modular form 1290.2.a.l

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} - q^{7} + q^{8} + q^{9} + q^{10} - 4q^{11} - q^{12} - 5q^{13} - q^{14} - q^{15} + q^{16} - 8q^{17} + q^{18} - 5q^{19} + O(q^{20})\)  Toggle raw display