Properties

Label 306735.cd
Number of curves $1$
Conductor $306735$
CM no
Rank $1$

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

Elliptic curves in class 306735.cd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
306735.cd1 306735cd1 \([0, 1, 1, -6816, 1974275]\) \(-4096/195\) \(-1667442382875555\) \([]\) \(2399040\) \(1.6008\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 306735.cd1 has rank \(1\).

Complex multiplication

The elliptic curves in class 306735.cd do not have complex multiplication.

Modular form 306735.2.a.cd

sage: E.q_eigenform(10)
 
\(q + 2 q^{2} + q^{3} + 2 q^{4} - q^{5} + 2 q^{6} - 3 q^{7} + q^{9} - 2 q^{10} + 2 q^{12} - 6 q^{14} - q^{15} - 4 q^{16} - 5 q^{17} + 2 q^{18} + 2 q^{19} + O(q^{20})\) Copy content Toggle raw display