Properties

Label 100015.a
Number of curves $1$
Conductor $100015$
CM no
Rank $1$

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

Elliptic curves in class 100015.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
100015.a1 100015a1 \([0, 1, 1, -3811, 89295]\) \(-6122862569488384/500075\) \(-500075\) \([]\) \(34944\) \(0.53761\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 100015.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 100015.a do not have complex multiplication.

Modular form 100015.2.a.a

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