Properties

Label 51870.c
Number of curves $1$
Conductor $51870$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 51870.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
51870.c1 51870c1 \([1, 1, 0, -13188, -1978032]\) \(-253695042842616649/1534055250000000\) \(-1534055250000000\) \([]\) \(290304\) \(1.5976\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 51870.c1 has rank \(0\).

Complex multiplication

The elliptic curves in class 51870.c do not have complex multiplication.

Modular form 51870.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - q^{7} - q^{8} + q^{9} + q^{10} - q^{11} - q^{12} + q^{13} + q^{14} + q^{15} + q^{16} + 3 q^{17} - q^{18} - q^{19} + O(q^{20})\) Copy content Toggle raw display