Properties

Label 50025r
Number of curves $1$
Conductor $50025$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 50025r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
50025.s1 50025r1 \([0, 1, 1, -1283, -18031]\) \(14959673344/90045\) \(1406953125\) \([]\) \(39168\) \(0.59468\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 50025r1 has rank \(1\).

Complex multiplication

The elliptic curves in class 50025r do not have complex multiplication.

Modular form 50025.2.a.r

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{4} + 5 q^{7} + q^{9} - 2 q^{12} + 4 q^{13} + 4 q^{16} - 3 q^{17} - 7 q^{19} + O(q^{20})\) Copy content Toggle raw display