Elliptic curve isogeny class with Cremona label 49818bc (LMFDB label 49818.bf)

• Label: 49818bc
• Number of curves: $2$
• Conductor: $49818$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 49818bc have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 - T\)
\(19\)	\(1\)
\(23\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 4 T + 5 T^{2}\)	1.5.e
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(17\)	\( 1 + 7 T + 17 T^{2}\)	1.17.h
\(29\)	\( 1 - 5 T + 29 T^{2}\)	1.29.af
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 49818bc do not have complex multiplication.

Modular form 49818.2.a.bc

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 49818bc

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
49818.bf2	49818bc1	\([1, 0, 0, -21416513, 37419575649]\)	\(63964821056640625/1396665211752\)	\(23720351670961706057832\)	\([3]\)	\(3939840\)	\(3.0816\)	\(\Gamma_0(N)\)-optimal
49818.bf1	49818bc2	\([1, 0, 0, -204757583, -1112392277697]\)	\(55900396438928556625/875360193471018\)	\(14866735029396990809445738\)	\([]\)	\(11819520\)	\(3.6309\)