Properties

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

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Show commands: SageMath
E = EllipticCurve("bn1")
 
E.isogeny_class()
 

Elliptic curves in class 12870.bn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
12870.bn1 12870be1 \([1, -1, 1, 172, -1383]\) \(20956092093/40842230\) \(-1102740210\) \([]\) \(6720\) \(0.41963\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 12870.bn1 has rank \(1\).

Complex multiplication

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

Modular form 12870.2.a.bn

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