Properties

Label 388311.i
Number of curves $1$
Conductor $388311$
CM no
Rank $2$

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

Elliptic curves in class 388311.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
388311.i1 388311i1 \([0, 1, 1, 55, -2863]\) \(10747904/2139291\) \(-3596148171\) \([]\) \(225792\) \(0.51283\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 388311.i1 has rank \(2\).

Complex multiplication

The elliptic curves in class 388311.i do not have complex multiplication.

Modular form 388311.2.a.i

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