Properties

Label 1288.i
Number of curves $1$
Conductor $1288$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 1288.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1288.i1 1288g1 \([0, 0, 0, -8419, 301667]\) \(-4124632486295808/70140333767\) \(-1122245340272\) \([]\) \(2688\) \(1.1107\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1288.i1 has rank \(0\).

Complex multiplication

The elliptic curves in class 1288.i do not have complex multiplication.

Modular form 1288.2.a.i

sage: E.q_eigenform(10)
 
\(q + 3 q^{3} + 2 q^{5} - q^{7} + 6 q^{9} + 2 q^{11} - q^{13} + 6 q^{15} + 2 q^{19} + O(q^{20})\) Copy content Toggle raw display