Elliptic curve isogeny class with Cremona label 254320bc (LMFDB label 254320.bc)

• Label: 254320bc
• Number of curves: $2$
• Conductor: $254320$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 254320bc have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1 - T\)
\(11\)	\(1 + T\)
\(17\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 + 10 T + 29 T^{2}\)	1.29.k
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 254320bc do not have complex multiplication.

Modular form 254320.2.a.bc

Isogeny matrix

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 254320bc

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
254320.bc1	254320bc1	\([0, 0, 0, -10982, 427431]\)	\(379275264/15125\)	\(5841291698000\)	\([2]\)	\(497664\)	\(1.2162\)	\(\Gamma_0(N)\)-optimal
254320.bc2	254320bc2	\([0, 0, 0, 4913, 1562334]\)	\(2122416/171875\)	\(-1062053036000000\)	\([2]\)	\(995328\)	\(1.5628\)