Elliptic curve isogeny class with Cremona label 20475w (LMFDB label 20475.bb)

• Label: 20475w
• Number of curves: $4$
• Conductor: $20475$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 20475w have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1 + T\)
\(13\)	\(1 - T\)

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
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 5 T + 23 T^{2}\)	1.23.f
\(29\)	\( 1 - 8 T + 29 T^{2}\)	1.29.ai
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 20475w do not have complex multiplication.

Modular form 20475.2.a.w

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 20475w

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
20475.bb3	20475w1	\([1, -1, 0, -52542, 3896991]\)	\(1408317602329/242911305\)	\(2766911583515625\)	\([2]\)	\(92160\)	\(1.6833\)	\(\Gamma_0(N)\)-optimal
20475.bb2	20475w2	\([1, -1, 0, -242667, -42303384]\)	\(138742439989609/12224619225\)	\(139246053359765625\)	\([2, 2]\)	\(184320\)	\(2.0299\)
20475.bb1	20475w3	\([1, -1, 0, -3796542, -2846310759]\)	\(531301262949272089/4740474375\)	\(53996965927734375\)	\([2]\)	\(368640\)	\(2.3764\)
20475.bb4	20475w4	\([1, -1, 0, 269208, -197401509]\)	\(189425802193991/1586486902455\)	\(-18071077373276484375\)	\([2]\)	\(368640\)	\(2.3764\)