Elliptic curve isogeny class with Cremona label 2700m (LMFDB label 2700.f)

• Label: 2700m
• Number of curves: $2$
• Conductor: $2700$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 2700m have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - T + 7 T^{2}\)	1.7.ab
\(11\)	\( 1 - 6 T + 11 T^{2}\)	1.11.ag
\(13\)	\( 1 - T + 13 T^{2}\)	1.13.ab
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + T + 19 T^{2}\)	1.19.b
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 2700m do not have complex multiplication.

Modular form 2700.2.a.m

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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

Elliptic curves in class 2700m

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
2700.f1	2700m1	\([0, 0, 0, -825, 9125]\)	\(-9199872/5\)	\(-33750000\)	\([]\)	\(864\)	\(0.39324\)	\(\Gamma_0(N)\)-optimal
2700.f2	2700m2	\([0, 0, 0, 675, 37125]\)	\(6912/125\)	\(-615093750000\)	\([]\)	\(2592\)	\(0.94254\)