Elliptic curve isogeny class with Cremona label 68544be (LMFDB label 68544.x)

• Label: 68544be
• Number of curves: $4$
• Conductor: $68544$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 68544be have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(11\)	\( 1 - 6 T + 11 T^{2}\)	1.11.ag
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 + 4 T + 29 T^{2}\)	1.29.e
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 68544be do not have complex multiplication.

Modular form 68544.2.a.be

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 68544be

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
68544.x4	68544be1	\([0, 0, 0, -25439196, -49844774320]\)	\(-152435594466395827792/1646846627220711\)	\(-19669830717340030058496\)	\([2]\)	\(4423680\)	\(3.0937\)	\(\Gamma_0(N)\)-optimal
68544.x3	68544be2	\([0, 0, 0, -408076716, -3172932212560]\)	\(157304700372188331121828/18069292138401\)	\(863273875465458745344\)	\([2, 2]\)	\(8847360\)	\(3.4403\)
68544.x2	68544be3	\([0, 0, 0, -409126476, -3155787112336]\)	\(79260902459030376659234/842751810121431609\)	\(80526189471796250930184192\)	\([2]\)	\(17694720\)	\(3.7869\)
68544.x1	68544be4	\([0, 0, 0, -6529227276, -203067673360144]\)	\(322159999717985454060440834/4250799\)	\(406170169638912\)	\([2]\)	\(17694720\)	\(3.7869\)