Properties

Label 123210.g
Number of curves $1$
Conductor $123210$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 123210.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
123210.g1 123210e1 \([1, -1, 0, -351405, 58596815]\) \(36963/10\) \(1298317780552819230\) \([]\) \(2344320\) \(2.1836\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 123210.g1 has rank \(1\).

Complex multiplication

The elliptic curves in class 123210.g do not have complex multiplication.

Modular form 123210.2.a.g

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - 3 q^{7} - q^{8} + q^{10} + 4 q^{11} - 5 q^{13} + 3 q^{14} + q^{16} - 2 q^{17} - 5 q^{19} + O(q^{20})\) Copy content Toggle raw display