Elliptic curve isogeny class with Cremona label 235950cd (LMFDB label 235950.cd)

• Label: 235950cd
• Number of curves: $4$
• Conductor: $235950$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 235950cd have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1 + T\)
\(5\)	\(1\)
\(11\)	\(1\)
\(13\)	\(1 + T\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 235950cd do not have complex multiplication.

Modular form 235950.2.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 235950cd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
235950.cd4	235950cd1	\([1, 1, 0, -872775, -518836875]\)	\(-2656166199049/2658140160\)	\(-73579022499840000000\)	\([2]\)	\(11059200\)	\(2.5078\)	\(\Gamma_0(N)\)-optimal
235950.cd3	235950cd2	\([1, 1, 0, -16360775, -25470004875]\)	\(17496824387403529/6580454400\)	\(182151193395600000000\)	\([2, 2]\)	\(22118400\)	\(2.8544\)
235950.cd2	235950cd3	\([1, 1, 0, -18780775, -17442864875]\)	\(26465989780414729/10571870144160\)	\(292636138194659902500000\)	\([2]\)	\(44236800\)	\(3.2009\)
235950.cd1	235950cd4	\([1, 1, 0, -261748775, -1630062136875]\)	\(71647584155243142409/10140000\)	\(280681695937500000\)	\([2]\)	\(44236800\)	\(3.2009\)