Properties

Label 5040j
Number of curves $1$
Conductor $5040$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 5040j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5040.a1 5040j1 \([0, 0, 0, -3708, 89532]\) \(-30211716096/1071875\) \(-200037600000\) \([]\) \(6720\) \(0.94078\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 5040j1 has rank \(0\).

Complex multiplication

The elliptic curves in class 5040j do not have complex multiplication.

Modular form 5040.2.a.j

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