Properties

Label 1840.e
Number of curves $1$
Conductor $1840$
CM no
Rank $1$

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

Elliptic curves in class 1840.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1840.e1 1840g1 \([0, 0, 0, -8, 12]\) \(-221184/115\) \(-29440\) \([]\) \(144\) \(-0.43807\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1840.e1 has rank \(1\).

Complex multiplication

The elliptic curves in class 1840.e do not have complex multiplication.

Modular form 1840.2.a.e

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