Properties

Label 575.c
Number of curves $1$
Conductor $575$
CM no
Rank $1$

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

Elliptic curves in class 575.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
575.c1 575d1 \([1, -1, 1, -55, 72]\) \(46305/23\) \(8984375\) \([]\) \(60\) \(0.027223\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 575.c1 has rank \(1\).

Complex multiplication

The elliptic curves in class 575.c do not have complex multiplication.

Modular form 575.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} + q^{7} + 3 q^{8} - 3 q^{9} - q^{11} + q^{13} - q^{14} - q^{16} + 3 q^{18} - 5 q^{19} + O(q^{20})\) Copy content Toggle raw display