Elliptic curve isogeny class with LMFDB label 126350.y (Cremona label 126350k)

• Label: 126350.y
• Number of curves: $4$
• Conductor: $126350$
• CM: no
• Rank: $0$

Elliptic curves in class 126350.y

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
126350.y1	126350k4	\([1, -1, 0, -51218567, 141100532341]\)	\(20214562937713929/665000\)	\(488836107265625000\)	\([2]\)	\(8294400\)	\(2.8949\)
126350.y2	126350k2	\([1, -1, 0, -3205567, 2198923341]\)	\(4955605568649/28302400\)	\(20804864725225000000\)	\([2, 2]\)	\(4147200\)	\(2.5483\)
126350.y3	126350k3	\([1, -1, 0, -1400567, 4659138341]\)	\(-413327139849/12516028840\)	\(-9200431303112625625000\)	\([2]\)	\(8294400\)	\(2.8949\)
126350.y4	126350k1	\([1, -1, 0, -317567, -10396659]\)	\(4818245769/2723840\)	\(2002272695360000000\)	\([2]\)	\(2073600\)	\(2.2017\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 126350.y have rank \(0\).

Complex multiplication

The elliptic curves in class 126350.y do not have complex multiplication.

Modular form 126350.2.a.y

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.