Properties

Label 253575.o
Number of curves $1$
Conductor $253575$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("o1")
 
E.isogeny_class()
 

Elliptic curves in class 253575.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
253575.o1 253575o1 \([0, 0, 1, -1106175, 508958406]\) \(-111701610496/18862875\) \(-25278056557154296875\) \([]\) \(8626176\) \(2.4498\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 253575.o1 has rank \(1\).

Complex multiplication

The elliptic curves in class 253575.o do not have complex multiplication.

Modular form 253575.2.a.o

sage: E.q_eigenform(10)
 
\(q - 2 q^{2} + 2 q^{4} + 2 q^{11} - 6 q^{13} - 4 q^{16} - q^{17} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display