Elliptic curve isogeny class with Cremona label 99960be (LMFDB label 99960.cq)

• Label: 99960be
• Number of curves: $4$
• Conductor: $99960$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 99960be have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(5\)	\(1 - T\)
\(7\)	\(1\)
\(17\)	\(1 - T\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 99960be do not have complex multiplication.

Modular form 99960.2.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 99960be

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
99960.cq3	99960be1	\([0, 1, 0, -112471, -14555626]\)	\(83587439220736/6885\)	\(12960213840\)	\([2]\)	\(294912\)	\(1.3840\)	\(\Gamma_0(N)\)-optimal
99960.cq2	99960be2	\([0, 1, 0, -112716, -14489280]\)	\(5258429611216/47403225\)	\(1427697156614400\)	\([2, 2]\)	\(589824\)	\(1.7305\)
99960.cq4	99960be3	\([0, 1, 0, -33336, -34429536]\)	\(-34008619684/4228250625\)	\(-509388244767360000\)	\([2]\)	\(1179648\)	\(2.0771\)
99960.cq1	99960be4	\([0, 1, 0, -196016, 9701040]\)	\(6913728144004/3658971285\)	\(440805696213980160\)	\([2]\)	\(1179648\)	\(2.0771\)