Elliptic curve isogeny class with Cremona label 97104r (LMFDB label 97104.cp)

• Label: 97104r
• Number of curves: $4$
• Conductor: $97104$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 97104r have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(7\)	\(1 - T\)
\(17\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(11\)	\( 1 + T + 11 T^{2}\)	1.11.b
\(13\)	\( 1 - T + 13 T^{2}\)	1.13.ab
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 10 T + 29 T^{2}\)	1.29.k
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 97104r do not have complex multiplication.

Modular form 97104.2.a.r

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 97104r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
97104.cp4	97104r1	\([0, 1, 0, -204220212, -1133805926340]\)	\(-152435594466395827792/1646846627220711\)	\(-10176223768821040637839104\)	\([2]\)	\(19906560\)	\(3.6145\)	\(\Gamma_0(N)\)-optimal
97104.cp3	97104r2	\([0, 1, 0, -3275949192, -72170610317820]\)	\(157304700372188331121828/18069292138401\)	\(446616356630335167661056\)	\([2, 2]\)	\(39813120\)	\(3.9610\)
97104.cp2	97104r3	\([0, 1, 0, -3284376432, -71780641472268]\)	\(79260902459030376659234/842751810121431609\)	\(41660374971762593466405931008\)	\([2]\)	\(79626240\)	\(4.3076\)
97104.cp1	97104r4	\([0, 1, 0, -52415185632, -4618866912554412]\)	\(322159999717985454060440834/4250799\)	\(210132898135308288\)	\([2]\)	\(79626240\)	\(4.3076\)