Properties

Label 87514.e
Number of curves $1$
Conductor $87514$
CM no
Rank $1$

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

Elliptic curves in class 87514.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
87514.e1 87514f1 \([1, 1, 0, -466, 6308]\) \(-95443993/100016\) \(-11766782384\) \([]\) \(73728\) \(0.62758\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 87514.e1 has rank \(1\).

Complex multiplication

The elliptic curves in class 87514.e do not have complex multiplication.

Modular form 87514.2.a.e

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