Properties

Label 67760.a
Number of curves $1$
Conductor $67760$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 67760.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
67760.a1 67760bg1 \([0, 0, 0, 3872, 282172]\) \(14155776/84035\) \(-38111520930560\) \([]\) \(285600\) \(1.2879\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 67760.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 67760.a do not have complex multiplication.

Modular form 67760.2.a.a

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