Elliptic curve isogeny class with LMFDB label 3600.u (Cremona label 3600bf)

• Label: 3600.u
• Number of curves: $8$
• Conductor: $3600$
• CM: no
• Rank: $1$

Elliptic curves in class 3600.u

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
3600.u1	3600bf7	\([0, 0, 0, -7776075, -8346199750]\)	\(1114544804970241/405\)	\(18895680000000\)	\([2]\)	\(49152\)	\(2.3380\)
3600.u2	3600bf5	\([0, 0, 0, -486075, -130369750]\)	\(272223782641/164025\)	\(7652750400000000\)	\([2, 2]\)	\(24576\)	\(1.9915\)
3600.u3	3600bf8	\([0, 0, 0, -396075, -180139750]\)	\(-147281603041/215233605\)	\(-10041939074880000000\)	\([2]\)	\(49152\)	\(2.3380\)
3600.u4	3600bf4	\([0, 0, 0, -288075, 59512250]\)	\(56667352321/15\)	\(699840000000\)	\([4]\)	\(12288\)	\(1.6449\)
3600.u5	3600bf3	\([0, 0, 0, -36075, -1219750]\)	\(111284641/50625\)	\(2361960000000000\)	\([2, 2]\)	\(12288\)	\(1.6449\)
3600.u6	3600bf2	\([0, 0, 0, -18075, 922250]\)	\(13997521/225\)	\(10497600000000\)	\([2, 2]\)	\(6144\)	\(1.2983\)
3600.u7	3600bf1	\([0, 0, 0, -75, 40250]\)	\(-1/15\)	\(-699840000000\)	\([2]\)	\(3072\)	\(0.95175\)	\(\Gamma_0(N)\)-optimal
3600.u8	3600bf6	\([0, 0, 0, 125925, -9157750]\)	\(4733169839/3515625\)	\(-164025000000000000\)	\([2]\)	\(24576\)	\(1.9915\)

Rank

The elliptic curves in class 3600.u have rank \(1\).

Complex multiplication

The elliptic curves in class 3600.u do not have complex multiplication.

Modular form 3600.2.a.u

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 16 & 4 & 8 & 16 & 8 \\ 2 & 1 & 2 & 8 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 16 & 4 & 8 & 16 & 8 \\ 16 & 8 & 16 & 1 & 4 & 2 & 4 & 8 \\ 4 & 2 & 4 & 4 & 1 & 2 & 4 & 2 \\ 8 & 4 & 8 & 2 & 2 & 1 & 2 & 4 \\ 16 & 8 & 16 & 4 & 4 & 2 & 1 & 8 \\ 8 & 4 & 8 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.