Elliptic curve isogeny class with Cremona label 25350c (LMFDB label 25350.r)

• Label: 25350c
• Number of curves: $4$
• Conductor: $25350$
• CM: no
• Rank: $1$

Elliptic curves in class 25350c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
25350.r4	25350c1	\([1, 1, 0, 16889350, 1013572500]\)	\(7064514799444439/4094064000000\)	\(-308769765027750000000000\)	\([2]\)	\(2903040\)	\(3.1967\)	\(\Gamma_0(N)\)-optimal
25350.r3	25350c2	\([1, 1, 0, -67610650, 8027072500]\)	\(453198971846635561/261896250564000\)	\(19751924676383910562500000\)	\([2]\)	\(5806080\)	\(3.5433\)
25350.r2	25350c3	\([1, 1, 0, -225520025, -1406229886875]\)	\(-16818951115904497561/1592332281446400\)	\(-120091934173062758400000000\)	\([2]\)	\(8709120\)	\(3.7460\)
25350.r1	25350c4	\([1, 1, 0, -3686640025, -86158675326875]\)	\(73474353581350183614361/576510977802240\)	\(43479818378978941440000000\)	\([2]\)	\(17418240\)	\(4.0926\)

Rank

The elliptic curves in class 25350c have rank \(1\).

Complex multiplication

The elliptic curves in class 25350c do not have complex multiplication.

Modular form 25350.2.a.c

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.