Properties

Label 2450r
Number of curves $1$
Conductor $2450$
CM no
Rank $1$

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

Elliptic curves in class 2450r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2450.c1 2450r1 \([1, -1, 0, 18758, -18059084]\) \(1323/256\) \(-141237624500000000\) \([]\) \(40320\) \(1.9700\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 2450r1 has rank \(1\).

Complex multiplication

The elliptic curves in class 2450r do not have complex multiplication.

Modular form 2450.2.a.r

sage: E.q_eigenform(10)
 
\(q - q^{2} - 3 q^{3} + q^{4} + 3 q^{6} - q^{8} + 6 q^{9} - 3 q^{12} - 2 q^{13} + q^{16} - 2 q^{17} - 6 q^{18} + 2 q^{19} + O(q^{20})\) Copy content Toggle raw display