Properties

Label 1380.e
Number of curves $1$
Conductor $1380$
CM no
Rank $1$

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

Elliptic curves in class 1380.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1380.e1 1380e1 \([0, 1, 0, -845, 12975]\) \(-260956266496/145546875\) \(-37260000000\) \([]\) \(1344\) \(0.73178\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1380.e1 has rank \(1\).

Complex multiplication

The elliptic curves in class 1380.e do not have complex multiplication.

Modular form 1380.2.a.e

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} - 3 q^{7} + q^{9} - 2 q^{11} - 2 q^{13} + q^{15} - 7 q^{17} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display