Elliptic curve isogeny class with Cremona label 79200bf (LMFDB label 79200.f)

• Label: 79200bf
• Number of curves: $2$
• Conductor: $79200$
• CM: no
• Rank: $2$

Rank

The elliptic curves in class 79200bf have rank \(2\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(13\)	\( 1 + T + 13 T^{2}\)	1.13.b
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 + T + 19 T^{2}\)	1.19.b
\(23\)	\( 1 - 3 T + 23 T^{2}\)	1.23.ad
\(29\)	\( 1 + 5 T + 29 T^{2}\)	1.29.f
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 79200bf do not have complex multiplication.

Modular form 79200.2.a.bf

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.

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

Isogeny graph

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

Elliptic curves in class 79200bf

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
79200.f2	79200bf1	\([0, 0, 0, 2175, 51500]\)	\(1560896/2475\)	\(-1804275000000\)	\([2]\)	\(98304\)	\(1.0370\)	\(\Gamma_0(N)\)-optimal
79200.f1	79200bf2	\([0, 0, 0, -14700, 524000]\)	\(7529536/1815\)	\(84680640000000\)	\([2]\)	\(196608\)	\(1.3835\)