Elliptic curve isogeny class with Cremona label 63580d (LMFDB label 63580.m)

• Label: 63580d
• Number of curves: $4$
• Conductor: $63580$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 63580d have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 2 T + 3 T^{2}\)	1.3.c
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 63580d do not have complex multiplication.

Modular form 63580.2.a.d

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 63580d

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
63580.m4	63580d1	\([0, -1, 0, -13101, 569726]\)	\(643956736/15125\)	\(5841291698000\)	\([2]\)	\(186624\)	\(1.2352\)	\(\Gamma_0(N)\)-optimal
63580.m3	63580d2	\([0, -1, 0, -28996, -1064280]\)	\(436334416/171875\)	\(1062053036000000\)	\([2]\)	\(373248\)	\(1.5818\)
63580.m2	63580d3	\([0, -1, 0, -128701, -17504334]\)	\(610462990336/8857805\)	\(3420894070016720\)	\([2]\)	\(559872\)	\(1.7845\)
63580.m1	63580d4	\([0, -1, 0, -2051996, -1130707480]\)	\(154639330142416/33275\)	\(205613467769600\)	\([2]\)	\(1119744\)	\(2.1311\)