Elliptic curve isogeny class with LMFDB label 30258.f (Cremona label 30258g)

• Label: 30258.f
• Number of curves: $4$
• Conductor: $30258$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 30258.f have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1\)
\(41\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 30258.f do not have complex multiplication.

Modular form 30258.2.a.f

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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 30258.f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
30258.f1	30258g4	\([1, -1, 0, -6641946, 6589902874]\)	\(9357915116017/538002\)	\(1863007309180665378\)	\([2]\)	\(1290240\)	\(2.5692\)
30258.f2	30258g2	\([1, -1, 0, -439056, 90514732]\)	\(2703045457/544644\)	\(1886007399417463716\)	\([2, 2]\)	\(645120\)	\(2.2227\)
30258.f3	30258g1	\([1, -1, 0, -136476, -18111488]\)	\(81182737/5904\)	\(20444524654931856\)	\([2]\)	\(322560\)	\(1.8761\)	\(\Gamma_0(N)\)-optimal
30258.f4	30258g3	\([1, -1, 0, 922554, 539573710]\)	\(25076571983/50863698\)	\(-176132135467819805922\)	\([2]\)	\(1290240\)	\(2.5692\)