Elliptic curve isogeny class with Cremona label 124215cd (LMFDB label 124215.y)

• Label: 124215cd
• Number of curves: $4$
• Conductor: $124215$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 124215cd have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1 - T\)
\(5\)	\(1 - T\)
\(7\)	\(1\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + 2 T^{2}\)	1.2.a
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - 3 T + 23 T^{2}\)	1.23.ad
\(29\)	\( 1 - 8 T + 29 T^{2}\)	1.29.ai
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 124215cd do not have complex multiplication.

Modular form 124215.2.a.cd

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 124215cd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
124215.y3	124215cd1	\([1, 0, 0, -1933786, 867027251]\)	\(1408317602329/242911305\)	\(137941861082653223505\)	\([2]\)	\(3870720\)	\(2.5847\)	\(\Gamma_0(N)\)-optimal
124215.y2	124215cd2	\([1, 0, 0, -8931231, -9459802080]\)	\(138742439989609/12224619225\)	\(6941985375786779088225\)	\([2, 2]\)	\(7741440\)	\(2.9313\)
124215.y4	124215cd3	\([1, 0, 0, 9908044, -44060014545]\)	\(189425802193991/1586486902455\)	\(-900917130669963776660655\)	\([2]\)	\(15482880\)	\(3.2778\)
124215.y1	124215cd4	\([1, 0, 0, -139729626, -635748677019]\)	\(531301262949272089/4740474375\)	\(2691969637650776949375\)	\([2]\)	\(15482880\)	\(3.2778\)