Elliptic curve isogeny class with Cremona label 12100e (LMFDB label 12100.d)

• Label: 12100e
• Number of curves: $2$
• Conductor: $12100$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 12100e have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1\)
\(11\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 8 T + 29 T^{2}\)	1.29.i
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 12100e do not have complex multiplication.

Modular form 12100.2.a.e

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 12100e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
12100.d2	12100e1	\([0, -1, 0, 8067, 317737]\)	\(8192/11\)	\(-77948684000000\)	\([]\)	\(25920\)	\(1.3514\)	\(\Gamma_0(N)\)-optimal
12100.d1	12100e2	\([0, -1, 0, -233933, 43877737]\)	\(-199794688/1331\)	\(-9431790764000000\)	\([]\)	\(77760\)	\(1.9007\)