Properties

Label 1911.e
Number of curves $1$
Conductor $1911$
CM no
Rank $1$

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

Elliptic curves in class 1911.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1911.e1 1911e1 \([0, 1, 1, 5, 88]\) \(32768/9477\) \(-3250611\) \([]\) \(192\) \(-0.071311\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1911.e1 has rank \(1\).

Complex multiplication

The elliptic curves in class 1911.e do not have complex multiplication.

Modular form 1911.2.a.e

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