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Properties

Label 55506.b
Number of curves $1$
Conductor $55506$
CM no
Rank $0$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("b1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 55506.b1 has rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 + T\)
\(3\)\(1 + T\)
\(11\)\(1 + T\)
\(29\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(5\) \( 1 + 3 T + 5 T^{2}\) 1.5.d
\(7\) \( 1 + T + 7 T^{2}\) 1.7.b
\(13\) \( 1 - T + 13 T^{2}\) 1.13.ab
\(17\) \( 1 + 4 T + 17 T^{2}\) 1.17.e
\(19\) \( 1 + T + 19 T^{2}\) 1.19.b
\(23\) \( 1 + 23 T^{2}\) 1.23.a
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 55506.b do not have complex multiplication.

Modular form 55506.2.a.b

Copy content sage:E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - 3 q^{5} + q^{6} - q^{7} - q^{8} + q^{9} + 3 q^{10} - q^{11} - q^{12} + q^{13} + q^{14} + 3 q^{15} + q^{16} - 4 q^{17} - q^{18} - q^{19} + O(q^{20})\) Copy content Toggle raw display

Elliptic curves in class 55506.b

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
55506.b1 55506i1 \([1, 1, 0, 210450141, 2357773069581]\) \(71054140594037203/206648056479744\) \(-2997873520981267999711297536\) \([]\) \(30011520\) \(3.9557\) \(\Gamma_0(N)\)-optimal