Properties

Label 75810.c
Number of curves $1$
Conductor $75810$
CM no
Rank $1$

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

Elliptic curves in class 75810.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
75810.c1 75810a1 \([1, 1, 0, -10273526088, -402773373059778]\) \(-371620692159996346278931/2118619749253938210\) \(-683652529355875573834020235590\) \([]\) \(217694400\) \(4.5667\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 75810.c1 has rank \(1\).

Complex multiplication

The elliptic curves in class 75810.c do not have complex multiplication.

Modular form 75810.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - q^{7} - q^{8} + q^{9} + q^{10} - 3 q^{11} - q^{12} + 5 q^{13} + q^{14} + q^{15} + q^{16} + 4 q^{17} - q^{18} + O(q^{20})\) Copy content Toggle raw display