Properties

Label 49686.ci
Number of curves $1$
Conductor $49686$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("ci1")
 
E.isogeny_class()
 

Elliptic curves in class 49686.ci

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
49686.ci1 49686cb1 \([1, 1, 1, -62280, 6849513]\) \(-47045881/8736\) \(-4960905785830176\) \([]\) \(322560\) \(1.7362\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 49686.ci1 has rank \(1\).

Complex multiplication

The elliptic curves in class 49686.ci do not have complex multiplication.

Modular form 49686.2.a.ci

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