Properties

Label 8712l
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 8712l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8712.x1 8712l1 \([0, 0, 0, -4356, 143748]\) \(-27648/11\) \(-3636773800704\) \([]\) \(13440\) \(1.1190\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 8712.2.a.l

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