Properties

Label 227850.cg
Number of curves $1$
Conductor $227850$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("cg1")
 
E.isogeny_class()
 

Elliptic curves in class 227850.cg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
227850.cg1 227850jh1 \([1, 1, 0, -28237500, -58066821000]\) \(-1354547383894636849/8173828125000\) \(-15025667266845703125000\) \([]\) \(37065600\) \(3.0949\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 227850.cg1 has rank \(1\).

Complex multiplication

The elliptic curves in class 227850.cg do not have complex multiplication.

Modular form 227850.2.a.cg

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - q^{8} + q^{9} + 5 q^{11} - q^{12} - 6 q^{13} + q^{16} - 4 q^{17} - q^{18} - 5 q^{19} + O(q^{20})\) Copy content Toggle raw display