↑

Properties

Label 98553.d
Number of curves $1$
Conductor $98553$
CM no
Rank $2$

Related objects

Downloads

Learn more

Show commands: SageMath
Copy content sage:E = EllipticCurve("d1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 98553.d1 has rank \(2\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(3\)\(1 + T\)
\(7\)\(1 + T\)
\(13\)\(1 - T\)
\(19\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(2\) \( 1 + T + 2 T^{2}\) 1.2.b
\(5\) \( 1 + 5 T^{2}\) 1.5.a
\(11\) \( 1 + 5 T + 11 T^{2}\) 1.11.f
\(17\) \( 1 + 5 T + 17 T^{2}\) 1.17.f
\(23\) \( 1 - 2 T + 23 T^{2}\) 1.23.ac
\(29\) \( 1 - 5 T + 29 T^{2}\) 1.29.af
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 98553.d do not have complex multiplication.

Modular form 98553.2.a.d

Copy content sage:E.q_eigenform(10)
 
\(q - q^{2} - q^{3} - q^{4} + q^{6} - q^{7} + 3 q^{8} + q^{9} - 5 q^{11} + q^{12} + q^{13} + q^{14} - q^{16} - 5 q^{17} - q^{18} + O(q^{20})\) Copy content Toggle raw display

Elliptic curves in class 98553.d

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
98553.d1 98553f1 \([1, 1, 1, -188, -1726]\) \(-5640625/5733\) \(-747130293\) \([]\) \(35136\) \(0.39818\) \(\Gamma_0(N)\)-optimal