Properties

Label 12870.bs
Number of curves $1$
Conductor $12870$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("bs1")
 
E.isogeny_class()
 

Elliptic curves in class 12870.bs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
12870.bs1 12870bt1 \([1, -1, 1, 4702342, 1889166777]\) \(15773893582068027616679/11245977600000000000\) \(-8198317670400000000000\) \([]\) \(1429120\) \(2.8933\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 12870.bs1 has rank \(0\).

Complex multiplication

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

Modular form 12870.2.a.bs

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