Elliptic curve isogeny class with Cremona label 355740d (LMFDB label 355740.d)

• Label: 355740d
• Number of curves: $2$
• Conductor: $355740$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 355740d have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(5\)	\(1 + T\)
\(7\)	\(1\)
\(11\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 355740d do not have complex multiplication.

Modular form 355740.2.a.d

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 355740d

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
355740.d2	355740d1	\([0, -1, 0, -82441, -9612854]\)	\(-6373654528/441045\)	\(-4287983609392560\)	\([2]\)	\(1935360\)	\(1.7505\)	\(\Gamma_0(N)\)-optimal
355740.d1	355740d2	\([0, -1, 0, -1340236, -596751560]\)	\(1711503051568/7425\)	\(1155012420038400\)	\([2]\)	\(3870720\)	\(2.0970\)