Properties

Label 63175p
Number of curves $1$
Conductor $63175$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 63175p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
63175.o1 63175p1 \([0, -1, 1, -1583, 23068]\) \(622592/49\) \(34548828125\) \([]\) \(51840\) \(0.76599\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 63175p1 has rank \(1\).

Complex multiplication

The elliptic curves in class 63175p do not have complex multiplication.

Modular form 63175.2.a.p

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