Properties

Label 2888.e
Number of curves $1$
Conductor $2888$
CM no
Rank $1$

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

Elliptic curves in class 2888.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2888.e1 2888a1 \([0, 1, 0, -153184, 23025409]\) \(1462911232\) \(271737008656\) \([]\) \(9576\) \(1.5090\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 2888.e1 has rank \(1\).

Complex multiplication

The elliptic curves in class 2888.e do not have complex multiplication.

Modular form 2888.2.a.e

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