Elliptic curve isogeny class with LMFDB label 70980.x (Cremona label 70980bb)

• Label: 70980.x
• Number of curves: $2$
• Conductor: $70980$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 70980.x have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1 - T\)
\(7\)	\(1 + T\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - 6 T + 19 T^{2}\)	1.19.ag
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 70980.x do not have complex multiplication.

Modular form 70980.2.a.x

Isogeny matrix

The \((i,j)\)-th 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 70980.x

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
70980.x1	70980bb2	\([0, 1, 0, -420, -3132]\)	\(14602768/1575\)	\(885830400\)	\([2]\)	\(29952\)	\(0.45087\)
70980.x2	70980bb1	\([0, 1, 0, 35, -220]\)	\(131072/735\)	\(-25836720\)	\([2]\)	\(14976\)	\(0.10430\)	\(\Gamma_0(N)\)-optimal