Properties

Label 10115.m
Number of curves $1$
Conductor $10115$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 10115.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10115.m1 10115b1 \([0, 1, 1, -96, 5745]\) \(-4096/595\) \(-14361853555\) \([]\) \(8064\) \(0.62838\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 10115.m1 has rank \(1\).

Complex multiplication

The elliptic curves in class 10115.m do not have complex multiplication.

Modular form 10115.2.a.m

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