Properties

Label 383040.ho
Number of curves $1$
Conductor $383040$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("ho1")
 
E.isogeny_class()
 

Elliptic curves in class 383040.ho

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
383040.ho1 383040ho1 \([0, 0, 0, 683988, 168084016]\) \(185183253170999/171032148000\) \(-32684752474472448000\) \([]\) \(8847360\) \(2.4317\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 383040.ho1 has rank \(1\).

Complex multiplication

The elliptic curves in class 383040.ho do not have complex multiplication.

Modular form 383040.2.a.ho

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