Properties

Label 274890.cf
Number of curves $1$
Conductor $274890$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("cf1")
 
E.isogeny_class()
 

Elliptic curves in class 274890.cf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
274890.cf1 274890cf1 \([1, 0, 1, -207884, -37433014]\) \(-8444922396903721/253364474880\) \(-29808077105157120\) \([]\) \(3326400\) \(1.9392\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 274890.cf1 has rank \(1\).

Complex multiplication

The elliptic curves in class 274890.cf do not have complex multiplication.

Modular form 274890.2.a.cf

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} - q^{8} + q^{9} + q^{10} + q^{11} + q^{12} + q^{13} - q^{15} + q^{16} + q^{17} - q^{18} + 5 q^{19} + O(q^{20})\) Copy content Toggle raw display