Properties

Label 412224.i
Number of curves $1$
Conductor $412224$
CM no
Rank $1$

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

Elliptic curves in class 412224.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
412224.i1 412224i1 \([0, -1, 0, -218276289, -536405363775]\) \(4387362075365553105987313/2064688435007280119808\) \(541245685106548439726948352\) \([]\) \(156764160\) \(3.8239\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 412224.i1 has rank \(1\).

Complex multiplication

The elliptic curves in class 412224.i do not have complex multiplication.

Modular form 412224.2.a.i

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