Properties

Label 115.a
Number of curves $1$
Conductor $115$
CM no
Rank $0$

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Show commands: SageMath
sage: E = EllipticCurve("a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 115.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115.a1 115a1 \([0, 0, 1, 7, -11]\) \(37933056/71875\) \(-71875\) \([]\) \(10\) \(-0.38348\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 115.a1 has rank \(0\).

Complex multiplication

The elliptic curves in class 115.a do not have complex multiplication.

Modular form 115.2.a.a

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