Properties

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

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("cd1")
 
E.isogeny_class()
 

Elliptic curves in class 12870.cd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
12870.cd1 12870bk1 \([1, -1, 1, -2, -11231]\) \(-27/2768480\) \(-54491991840\) \([]\) \(14400\) \(0.73899\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 12870.cd1 has rank \(0\).

Complex multiplication

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

Modular form 12870.2.a.cd

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