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Properties

Label 35490.cj
Number of curves $1$
Conductor $35490$
CM no
Rank $1$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("cj1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 35490.cj1 has rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 - T\)
\(3\)\(1 + T\)
\(5\)\(1 - T\)
\(7\)\(1 + T\)
\(13\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(11\) \( 1 + 5 T + 11 T^{2}\) 1.11.f
\(17\) \( 1 - 7 T + 17 T^{2}\) 1.17.ah
\(19\) \( 1 + T + 19 T^{2}\) 1.19.b
\(23\) \( 1 - 4 T + 23 T^{2}\) 1.23.ae
\(29\) \( 1 + 3 T + 29 T^{2}\) 1.29.d
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 35490.cj do not have complex multiplication.

Modular form 35490.2.a.cj

Copy content sage:E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} - q^{7} + q^{8} + q^{9} + q^{10} - 5 q^{11} - q^{12} - q^{14} - q^{15} + q^{16} + 7 q^{17} + q^{18} - q^{19} + O(q^{20})\) Copy content Toggle raw display

Elliptic curves in class 35490.cj

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
35490.cj1 35490cr1 \([1, 1, 1, -790, -8845]\) \(322665579769/1360800\) \(229975200\) \([]\) \(28800\) \(0.45886\) \(\Gamma_0(N)\)-optimal