Properties

Label 6762.l
Number of curves $1$
Conductor $6762$
CM no
Rank $1$

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

Elliptic curves in class 6762.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6762.l1 6762q1 \([1, 0, 1, -251445, 48748480]\) \(-14943832855786297/85501108224\) \(-10059119881445376\) \([]\) \(74880\) \(1.9124\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 6762.l1 has rank \(1\).

Complex multiplication

The elliptic curves in class 6762.l do not have complex multiplication.

Modular form 6762.2.a.l

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - 3q^{5} - q^{6} - q^{8} + q^{9} + 3q^{10} + 4q^{11} + q^{12} - 3q^{13} - 3q^{15} + q^{16} - q^{18} + O(q^{20})\)  Toggle raw display