Elliptic curve isogeny class with Cremona label 305760i (LMFDB label 305760.i)

• Label: 305760i
• Number of curves: $4$
• Conductor: $305760$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 305760i have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(5\)	\(1 + T\)
\(7\)	\(1\)
\(13\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 - 4 T + 23 T^{2}\)	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 305760i do not have complex multiplication.

Modular form 305760.2.a.i

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 305760i

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
305760.i3	305760i1	\([0, -1, 0, -211206, 15424200]\)	\(138380950431424/66556260225\)	\(501137757389505600\)	\([2, 2]\)	\(3932160\)	\(2.0900\)	\(\Gamma_0(N)\)-optimal
305760.i1	305760i2	\([0, -1, 0, -2791056, 1794488760]\)	\(39918233807262728/30351677265\)	\(1828272373017592320\)	\([2]\)	\(7864320\)	\(2.4366\)
305760.i4	305760i3	\([0, -1, 0, 761199, 116748801]\)	\(101220756956864/70849130625\)	\(-34141509095016960000\)	\([2]\)	\(7864320\)	\(2.4366\)
305760.i2	305760i4	\([0, -1, 0, -1771856, -896619660]\)	\(10212945793989128/137103806385\)	\(8258624367303098880\)	\([2]\)	\(7864320\)	\(2.4366\)