Properties

Label 420544.i
Number of curves $1$
Conductor $420544$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 420544.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
420544.i1 420544i1 \([0, -1, 0, -37, 165]\) \(-5619712/6571\) \(-6728704\) \([]\) \(168192\) \(0.0042120\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 420544.i1 has rank \(1\).

Complex multiplication

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

Modular form 420544.2.a.i

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