Properties

Label 245.a
Number of curves $1$
Conductor $245$
CM no
Rank $1$

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 245.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
245.a1 245a1 \([0, 0, 1, -7, 12]\) \(-110592/125\) \(-42875\) \([]\) \(48\) \(-0.41676\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 245.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 245.a do not have complex multiplication.

Modular form 245.2.a.a

sage: E.q_eigenform(10)
 
\(q - 2q^{2} - 3q^{3} + 2q^{4} + q^{5} + 6q^{6} + 6q^{9} - 2q^{10} + q^{11} - 6q^{12} - 3q^{13} - 3q^{15} - 4q^{16} + 3q^{17} - 12q^{18} - 6q^{19} + O(q^{20})\)  Toggle raw display