Elliptic curve isogeny class with Cremona label 277725ba (LMFDB label 277725.ba)

• Label: 277725ba
• Number of curves: $2$
• Conductor: $277725$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 277725ba have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(7\)	\(1 - T\)
\(23\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + T + 2 T^{2}\)	1.2.b
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 277725ba do not have complex multiplication.

Modular form 277725.2.a.ba

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 277725ba

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
277725.ba1	277725ba1	\([1, 0, 0, -15281763, 22992235392]\)	\(1365045221357/11109\)	\(3211974005666015625\)	\([2]\)	\(10137600\)	\(2.7221\)	\(\Gamma_0(N)\)-optimal
277725.ba2	277725ba2	\([1, 0, 0, -14951138, 24034696017]\)	\(-1278348920477/123409881\)	\(-35681819228943767578125\)	\([2]\)	\(20275200\)	\(3.0687\)