Properties

Label 225420bl
Number of curves $1$
Conductor $225420$
CM no
Rank $0$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("bl1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 225420bl1 has rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1 - T\)
\(5\)\(1 - T\)
\(13\)\(1 + T\)
\(17\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(7\) \( 1 + 7 T^{2}\) 1.7.a
\(11\) \( 1 + 6 T + 11 T^{2}\) 1.11.g
\(19\) \( 1 + 19 T^{2}\) 1.19.a
\(23\) \( 1 - 4 T + 23 T^{2}\) 1.23.ae
\(29\) \( 1 + 2 T + 29 T^{2}\) 1.29.c
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 225420bl do not have complex multiplication.

Modular form 225420.2.a.bl

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

Elliptic curves in class 225420bl

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
225420.d1 225420bl1 \([0, -1, 0, 499, 28905]\) \(10903552/296595\) \(-373035836160\) \([]\) \(283392\) \(0.90052\) \(\Gamma_0(N)\)-optimal