Elliptic curve isogeny class with LMFDB label 235200.bal (Cremona label 235200bal)

• Label: 235200.bal
• Number of curves: $4$
• Conductor: $235200$
• CM: no
• Rank: $2$

Rank

The elliptic curves in class 235200.bal have rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(7\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 8 T + 23 T^{2}\)	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 235200.bal do not have complex multiplication.

Modular form 235200.2.a.bal

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 LMFDB 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 LMFDB labels.

Elliptic curves in class 235200.bal

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
235200.bal1	235200bal3	\([0, 1, 0, -5489633, 4948828863]\)	\(303735479048/105\)	\(6324810240000000\)	\([2]\)	\(7077888\)	\(2.3878\)
235200.bal2	235200bal2	\([0, 1, 0, -344633, 76513863]\)	\(601211584/11025\)	\(83013134400000000\)	\([2, 2]\)	\(3538944\)	\(2.0413\)
235200.bal3	235200bal1	\([0, 1, 0, -44508, -1818762]\)	\(82881856/36015\)	\(4237128735000000\)	\([2]\)	\(1769472\)	\(1.6947\)	\(\Gamma_0(N)\)-optimal
235200.bal4	235200bal4	\([0, 1, 0, -1633, 222288863]\)	\(-8/354375\)	\(-21346234560000000000\)	\([2]\)	\(7077888\)	\(2.3878\)