Properties

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

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 388311.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
388311.e1 388311e1 \([1, 0, 0, -23073441, 42800730462]\) \(-285994494781134049/1111953921309\) \(-5281897037406461171469\) \([]\) \(24837120\) \(3.0264\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 388311.e1 has rank \(2\).

Complex multiplication

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

Modular form 388311.2.a.e

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