Properties

Label 286650.jd
Number of curves $1$
Conductor $286650$
CM no
Rank $0$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("jd1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 286650.jd1 has rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 - T\)
\(3\)\(1\)
\(5\)\(1\)
\(7\)\(1\)
\(13\)\(1 + T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(11\) \( 1 + 5 T + 11 T^{2}\) 1.11.f
\(17\) \( 1 - 2 T + 17 T^{2}\) 1.17.ac
\(19\) \( 1 - 2 T + 19 T^{2}\) 1.19.ac
\(23\) \( 1 + 8 T + 23 T^{2}\) 1.23.i
\(29\) \( 1 - 5 T + 29 T^{2}\) 1.29.af
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 286650.jd do not have complex multiplication.

Modular form 286650.2.a.jd

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

Elliptic curves in class 286650.jd

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
286650.jd1 286650jd1 \([1, -1, 1, -41377055, -91245522553]\) \(4772330903305/570306048\) \(936224194714918200000000\) \([]\) \(61689600\) \(3.3306\) \(\Gamma_0(N)\)-optimal