Elliptic curve isogeny class with LMFDB label 194040.ec (Cremona label 194040a)

• Label: 194040.ec
• Number of curves: $4$
• Conductor: $194040$
• CM: no
• Rank: $2$

Rank

The elliptic curves in class 194040.ec have rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 - T\)
\(7\)	\(1\)
\(11\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 194040.ec do not have complex multiplication.

Modular form 194040.2.a.ec

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 194040.ec

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
194040.ec1	194040a4	\([0, 0, 0, -3328227, -120263346]\)	\(46424454082884/26794860125\)	\(2353245404834636928000\)	\([2]\)	\(10616832\)	\(2.7904\)
194040.ec2	194040a2	\([0, 0, 0, -2225727, 1273517154]\)	\(55537159171536/228765625\)	\(5022807110244000000\)	\([2, 2]\)	\(5308416\)	\(2.4438\)
194040.ec3	194040a1	\([0, 0, 0, -2223522, 1276175061]\)	\(885956203616256/15125\)	\(20755401282000\)	\([2]\)	\(2654208\)	\(2.0972\)	\(\Gamma_0(N)\)-optimal
194040.ec4	194040a3	\([0, 0, 0, -1158507, 2497191606]\)	\(-1957960715364/29541015625\)	\(-2594425160250000000000\)	\([2]\)	\(10616832\)	\(2.7904\)