Properties

Label 413712dt
Number of curves $1$
Conductor $413712$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("dt1")
 
E.isogeny_class()
 

Elliptic curves in class 413712dt

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
413712.dt1 413712dt1 \([0, 0, 0, -624, 23920]\) \(-53248/459\) \(-231625764864\) \([]\) \(483840\) \(0.86333\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 413712dt1 has rank \(1\).

Complex multiplication

The elliptic curves in class 413712dt do not have complex multiplication.

Modular form 413712.2.a.dt

sage: E.q_eigenform(10)
 
\(q + 2 q^{5} - 4 q^{7} - 3 q^{11} - q^{17} + 7 q^{19} + O(q^{20})\) Copy content Toggle raw display