Properties

Label 3440.e
Number of curves $1$
Conductor $3440$
CM no
Rank $1$

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

Elliptic curves in class 3440.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3440.e1 3440a1 \([0, -1, 0, 0, 32]\) \(-2/215\) \(-440320\) \([]\) \(448\) \(-0.23817\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 3440.e1 has rank \(1\).

Complex multiplication

The elliptic curves in class 3440.e do not have complex multiplication.

Modular form 3440.2.a.e

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