Properties

Label 312312.bz
Number of curves $1$
Conductor $312312$
CM no
Rank $1$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("bz1")
 
E.isogeny_class()
 

Elliptic curves in class 312312.bz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
312312.bz1 312312bz1 \([0, 1, 0, -280596, 59160453]\) \(-31636584484096/1331669031\) \(-102843393021633264\) \([]\) \(3231360\) \(2.0309\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 312312.bz1 has rank \(1\).

Complex multiplication

The elliptic curves in class 312312.bz do not have complex multiplication.

Modular form 312312.2.a.bz

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} + q^{7} + q^{9} + q^{11} - q^{15} - 7 q^{19} + O(q^{20})\) Copy content Toggle raw display