Properties

Label 637.a
Number of curves $1$
Conductor $637$
CM no
Rank $1$

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

Elliptic curves in class 637.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
637.a1 637d1 \([0, 0, 1, 49, -86]\) \(110592/91\) \(-10706059\) \([]\) \(192\) \(0.036626\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 637.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 637.a do not have complex multiplication.

Modular form 637.2.a.a

sage: E.q_eigenform(10)
 
\(q - 2q^{2} + 2q^{4} + 3q^{5} - 3q^{9} - 6q^{10} - 6q^{11} + q^{13} - 4q^{16} - 4q^{17} + 6q^{18} - 5q^{19} + O(q^{20})\)  Toggle raw display