Properties

Label 8712.l
Number of curves $1$
Conductor $8712$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 8712.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8712.l1 8712h1 \([0, 0, 0, -79860, 9897316]\) \(-1408000/243\) \(-9721096369281792\) \([]\) \(42240\) \(1.7940\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 8712.l1 has rank \(1\).

Complex multiplication

The elliptic curves in class 8712.l do not have complex multiplication.

Modular form 8712.2.a.l

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