Elliptic curve isogeny class with Cremona label 234432ee (LMFDB label 234432.ee)

• Label: 234432ee
• Number of curves: $2$
• Conductor: $234432$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 234432ee have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(11\)	\(1 - T\)
\(37\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 - 8 T + 29 T^{2}\)	1.29.ai
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 234432ee do not have complex multiplication.

Modular form 234432.2.a.ee

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 234432ee

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
234432.ee1	234432ee1	\([0, 0, 0, -2123638104, -37667680442008]\)	\(1418854149881269000523696128/21413352213\)	\(15984981773595648\)	\([2]\)	\(71565312\)	\(3.5896\)	\(\Gamma_0(N)\)-optimal
234432.ee2	234432ee2	\([0, 0, 0, -2123636124, -37667754193840]\)	\(-88678136326676754811067728/344501617579257699\)	\(-4114705272263128884363264\)	\([2]\)	\(143130624\)	\(3.9362\)