Properties

Label 420544b
Number of curves $1$
Conductor $420544$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 420544b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
420544.b1 420544b1 \([0, 1, 0, -37, -165]\) \(-5619712/6571\) \(-6728704\) \([]\) \(168192\) \(0.0042120\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 420544b1 has rank \(1\).

Complex multiplication

The elliptic curves in class 420544b do not have complex multiplication.

Modular form 420544.2.a.b

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} + 2 q^{5} + 5 q^{7} + q^{9} - 6 q^{11} + 6 q^{13} - 4 q^{15} - 3 q^{17} - 8 q^{19} + O(q^{20})\) Copy content Toggle raw display