Elliptic curve isogeny class with Cremona label 308550hh (LMFDB label 308550.hh)

• Label: 308550hh
• Number of curves: $4$
• Conductor: $308550$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 308550hh have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 + T\)
\(5\)	\(1\)
\(11\)	\(1\)
\(17\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 308550hh do not have complex multiplication.

Modular form 308550.2.a.hh

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 308550hh

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
308550.hh4	308550hh1	\([1, 1, 1, -17687238, 22382670531]\)	\(22106889268753393/4969545596928\)	\(137560205738115072000000\)	\([2]\)	\(41287680\)	\(3.1528\)	\(\Gamma_0(N)\)-optimal
308550.hh2	308550hh2	\([1, 1, 1, -265495238, 1664854094531]\)	\(74768347616680342513/5615307472896\)	\(155435308156111104000000\)	\([2, 2]\)	\(82575360\)	\(3.4994\)
308550.hh1	308550hh3	\([1, 1, 1, -4247847238, 106560005774531]\)	\(306234591284035366263793/1727485056\)	\(47817893020194000000\)	\([2]\)	\(165150720\)	\(3.8459\)
308550.hh3	308550hh4	\([1, 1, 1, -248071238, 1892829710531]\)	\(-60992553706117024753/20624795251201152\)	\(-570907545312705688098000000\)	\([2]\)	\(165150720\)	\(3.8459\)