Elliptic curve isogeny class with Cremona label 67600cf (LMFDB label 67600.u)

• Label: 67600cf
• Number of curves: $4$
• Conductor: $67600$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 67600cf have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - T + 3 T^{2}\)	1.3.ab
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + T + 23 T^{2}\)	1.23.b
\(29\)	\( 1 - 5 T + 29 T^{2}\)	1.29.af
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 67600cf do not have complex multiplication.

Modular form 67600.2.a.cf

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 67600cf

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
67600.u2	67600cf1	\([0, 1, 0, -2198408, -1247916812]\)	\(3803721481/26000\)	\(8031810176000000000\)	\([2]\)	\(2322432\)	\(2.4615\)	\(\Gamma_0(N)\)-optimal
67600.u3	67600cf2	\([0, 1, 0, -846408, -2764860812]\)	\(-217081801/10562500\)	\(-3262922884000000000000\)	\([2]\)	\(4644864\)	\(2.8081\)
67600.u1	67600cf3	\([0, 1, 0, -14028408, 19407263188]\)	\(988345570681/44994560\)	\(13899529418178560000000\)	\([2]\)	\(6967296\)	\(3.0108\)
67600.u4	67600cf4	\([0, 1, 0, 7603592, 73876639188]\)	\(157376536199/7722894400\)	\(-2385723916542054400000000\)	\([2]\)	\(13934592\)	\(3.3574\)