Properties

Label 12870.j
Number of curves $1$
Conductor $12870$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 12870.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
12870.j1 12870d1 \([1, -1, 0, 0, 416]\) \(-27/2768480\) \(-74748960\) \([]\) \(4800\) \(0.18969\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 12870.j1 has rank \(1\).

Complex multiplication

The elliptic curves in class 12870.j do not have complex multiplication.

Modular form 12870.2.a.j

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