Properties

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

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 50025b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
50025.h1 50025b1 \([0, -1, 1, -264942783, -1659790506157]\) \(-131631542171643599790505984/44988384234391875\) \(-702943503662373046875\) \([]\) \(8386560\) \(3.3567\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 50025b1 has rank \(1\).

Complex multiplication

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

Modular form 50025.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2 q^{4} - 2 q^{7} + q^{9} - 4 q^{11} + 2 q^{12} + 5 q^{13} + 4 q^{16} - 7 q^{17} - 5 q^{19} + O(q^{20})\) Copy content Toggle raw display