Elliptic curve isogeny class with LMFDB label 62475.cm (Cremona label 62475bs)

• Label: 62475.cm
• Number of curves: $4$
• Conductor: $62475$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 62475.cm have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(7\)	\(1\)
\(17\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 - T + 2 T^{2}\)	1.2.ab
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 62475.cm do not have complex multiplication.

Modular form 62475.2.a.cm

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 62475.cm

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
62475.cm1	62475bs4	\([1, 0, 1, -2065376, -1142597977]\)	\(530044731605089/26309115\)	\(48363141728671875\)	\([2]\)	\(1179648\)	\(2.2728\)
62475.cm2	62475bs3	\([1, 0, 1, -656626, 190324523]\)	\(17032120495489/1339001685\)	\(2461440769352578125\)	\([2]\)	\(1179648\)	\(2.2728\)
62475.cm3	62475bs2	\([1, 0, 1, -136001, -15842977]\)	\(151334226289/28676025\)	\(52714151019140625\)	\([2, 2]\)	\(589824\)	\(1.9263\)
62475.cm4	62475bs1	\([1, 0, 1, 17124, -1449227]\)	\(302111711/669375\)	\(-1230489052734375\)	\([2]\)	\(294912\)	\(1.5797\)	\(\Gamma_0(N)\)-optimal