Elliptic curve isogeny class with LMFDB label 493680.gu (Cremona label 493680gu)

• Label: 493680.gu
• Number of curves: $4$
• Conductor: $493680$
• CM: no
• Rank: $0$

Elliptic curves in class 493680.gu

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
493680.gu1	493680gu3	\([0, 1, 0, -729692960, 7361739990900]\)	\(5921450764096952391481/200074809015963750\)	\(1451805608899091484318720000\)	\([2]\)	\(212336640\)	\(3.9842\)	\(\Gamma_0(N)\)-optimal^*
493680.gu2	493680gu2	\([0, 1, 0, -112592960, -300914129100]\)	\(21754112339458491481/7199734626562500\)	\(52243534130248454400000000\)	\([2, 2]\)	\(106168320\)	\(3.6376\)	\(\Gamma_0(N)\)-optimal^*
493680.gu3	493680gu1	\([0, 1, 0, -101402880, -392990583372]\)	\(15891267085572193561/3334993530000\)	\(24199759761409351680000\)	\([2]\)	\(53084160\)	\(3.2911\)	\(\Gamma_0(N)\)-optimal^*
493680.gu4	493680gu4	\([0, 1, 0, 325465760, -2070496134412]\)	\(525440531549759128199/559322204589843750\)	\(-4058617463133750000000000000\)	\([4]\)	\(212336640\)	\(3.9842\)

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 3 curves highlighted, and conditionally curve 493680.gu1.

Rank

The elliptic curves in class 493680.gu have rank \(0\).

Complex multiplication

The elliptic curves in class 493680.gu do not have complex multiplication.

Modular form 493680.2.a.gu

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.