Properties

Label 123627i
Number of curves $1$
Conductor $123627$
CM no
Rank $2$

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

Elliptic curves in class 123627i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
123627.g1 123627i1 \([1, 1, 1, -1569, 24156]\) \(-4317433/189\) \(-18700190901\) \([]\) \(86400\) \(0.73628\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 123627i1 has rank \(2\).

Complex multiplication

The elliptic curves in class 123627i do not have complex multiplication.

Modular form 123627.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} - q^{4} - 2 q^{5} + q^{6} + 3 q^{8} + q^{9} + 2 q^{10} + q^{11} + q^{12} - 4 q^{13} + 2 q^{15} - q^{16} + q^{17} - q^{18} - q^{19} + O(q^{20})\) Copy content Toggle raw display