Properties

Label 409101.e
Number of curves $1$
Conductor $409101$
CM no
Rank $0$

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

Elliptic curves in class 409101.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
409101.e1 409101e1 \([1, 1, 1, 180711, -51384684]\) \(1268071343/2956581\) \(-1521680316784812261\) \([]\) \(5464800\) \(2.1729\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 409101.e1 has rank \(0\).

Complex multiplication

The elliptic curves in class 409101.e do not have complex multiplication.

Modular form 409101.2.a.e

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