Properties

Label 69828.p
Number of curves $1$
Conductor $69828$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 69828.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
69828.p1 69828q1 \([0, -1, 0, -159842, -24543927]\) \(53360942198048512/2910897\) \(24637832208\) \([]\) \(302400\) \(1.4630\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 69828.p1 has rank \(0\).

Complex multiplication

The elliptic curves in class 69828.p do not have complex multiplication.

Modular form 69828.2.a.p

sage: E.q_eigenform(10)
 
\(q - q^{3} + 2 q^{5} - 4 q^{7} + q^{9} + q^{11} + 4 q^{13} - 2 q^{15} - 3 q^{17} + 6 q^{19} + O(q^{20})\) Copy content Toggle raw display