Elliptic curve isogeny class with Cremona label 6240r (LMFDB label 6240.bb)

• Label: 6240r
• Number of curves: $2$
• Conductor: $6240$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 6240r have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1 + T\)
\(13\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + T + 7 T^{2}\)	1.7.b
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 - 6 T + 19 T^{2}\)	1.19.ag
\(23\)	\( 1 - T + 23 T^{2}\)	1.23.ab
\(29\)	\( 1 - 8 T + 29 T^{2}\)	1.29.ai
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 6240r do not have complex multiplication.

Modular form 6240.2.a.r

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 6240r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
6240.bb1	6240r1	\([0, 1, 0, -10590, 415188]\)	\(2052450196928704/4317958125\)	\(276349320000\)	\([2]\)	\(9216\)	\(1.0805\)	\(\Gamma_0(N)\)-optimal
6240.bb2	6240r2	\([0, 1, 0, -6945, 708975]\)	\(-9045718037056/48125390625\)	\(-197121600000000\)	\([2]\)	\(18432\)	\(1.4271\)