Properties

Label 112710.cz
Number of curves $1$
Conductor $112710$
CM no
Rank $1$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("cz1")
 
E.isogeny_class()
 

Elliptic curves in class 112710.cz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
112710.cz1 112710dc1 \([1, 0, 0, -2949540, 1949997492]\) \(-406813373046721/118462500\) \(-826365665854462500\) \([]\) \(3231360\) \(2.4175\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 112710.cz1 has rank \(1\).

Complex multiplication

The elliptic curves in class 112710.cz do not have complex multiplication.

Modular form 112710.2.a.cz

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