Elliptic curve isogeny class with Cremona label 26010f (LMFDB label 26010.g)

• Label: 26010f
• Number of curves: $4$
• Conductor: $26010$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 26010f have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1\)
\(5\)	\(1 + T\)
\(17\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(19\)	\( 1 + 8 T + 19 T^{2}\)	1.19.i
\(23\)	\( 1 - 2 T + 23 T^{2}\)	1.23.ac
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 26010f do not have complex multiplication.

Modular form 26010.2.a.f

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.

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

Isogeny graph

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

Elliptic curves in class 26010f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
26010.g4	26010f1	\([1, -1, 0, 10350, 41476]\)	\(6967871/4080\)	\(-71792854228080\)	\([2]\)	\(73728\)	\(1.3481\)	\(\Gamma_0(N)\)-optimal
26010.g3	26010f2	\([1, -1, 0, -41670, 364000]\)	\(454756609/260100\)	\(4576794457040100\)	\([2, 2]\)	\(147456\)	\(1.6947\)
26010.g2	26010f3	\([1, -1, 0, -431820, -108643910]\)	\(506071034209/2505630\)	\(44089786602819630\)	\([2]\)	\(294912\)	\(2.0413\)
26010.g1	26010f4	\([1, -1, 0, -483840, 129389206]\)	\(711882749089/1721250\)	\(30287610377471250\)	\([2]\)	\(294912\)	\(2.0413\)