Properties

Label 30345.a
Number of curves $1$
Conductor $30345$
CM no
Rank $1$

Related objects

Downloads

Learn more

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

Elliptic curves in class 30345.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
30345.a1 30345o1 \([0, -1, 1, -76970, 8225408]\) \(7229403136/19845\) \(138433906416645\) \([]\) \(215424\) \(1.5866\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 30345.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 30345.a do not have complex multiplication.

Modular form 30345.2.a.a

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