Elliptic curve isogeny class with LMFDB label 155610.eh (Cremona label 155610u)

• Label: 155610.eh
• Number of curves: $4$
• Conductor: $155610$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 155610.eh have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1\)
\(5\)	\(1 - T\)
\(7\)	\(1 + T\)
\(13\)	\(1 - T\)
\(19\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 155610.eh do not have complex multiplication.

Modular form 155610.2.a.eh

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 155610.eh

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
155610.eh1	155610u3	\([1, -1, 1, -33196802, 73627734129]\)	\(5549896908024170183373529/56019600\)	\(40838288400\)	\([2]\)	\(5242880\)	\(2.5448\)
155610.eh2	155610u4	\([1, -1, 1, -2102882, 1118090481]\)	\(1410719602237262088409/76269550743750000\)	\(55600502492193750000\)	\([2]\)	\(5242880\)	\(2.5448\)
155610.eh3	155610u2	\([1, -1, 1, -2074802, 1150820529]\)	\(1354958399265695661529/4304795040000\)	\(3138195584160000\)	\([2, 2]\)	\(2621440\)	\(2.1983\)
155610.eh4	155610u1	\([1, -1, 1, -127922, 18515121]\)	\(-317562142497484249/18670942617600\)	\(-13611117168230400\)	\([4]\)	\(1310720\)	\(1.8517\)	\(\Gamma_0(N)\)-optimal