Properties

Label 75213c
Number of curves $1$
Conductor $75213$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 75213c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
75213.c1 75213c1 \([0, 0, 1, -219, 643]\) \(1593413632/676917\) \(493472493\) \([]\) \(71680\) \(0.36475\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 75213c1 has rank \(1\).

Complex multiplication

The elliptic curves in class 75213c do not have complex multiplication.

Modular form 75213.2.a.c

sage: E.q_eigenform(10)
 
\(q + 2 q^{2} + 2 q^{4} + 2 q^{5} - 4 q^{7} + 4 q^{10} + 6 q^{11} - 4 q^{13} - 8 q^{14} - 4 q^{16} + 6 q^{17} - 5 q^{19} + O(q^{20})\) Copy content Toggle raw display