Properties

Label 28322c
Number of curves $1$
Conductor $28322$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 28322c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
28322.b1 28322c1 \([1, -1, 0, -441646, 407309524]\) \(-164384733177/1140850688\) \(-66117206642914230272\) \([]\) \(1797120\) \(2.4864\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 28322c1 has rank \(1\).

Complex multiplication

The elliptic curves in class 28322c do not have complex multiplication.

Modular form 28322.2.a.c

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