Elliptic curve isogeny class with Cremona label 42350f (LMFDB label 42350.y)

• Label: 42350f
• Number of curves: $4$
• Conductor: $42350$
• CM: no
• Rank: $0$

Elliptic curves in class 42350f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
42350.y4	42350f1	\([1, -1, 0, -36569792, 102459087616]\)	\(-195395722614328041/50730248800000\)	\(-1404245785849637500000000\)	\([2]\)	\(7372800\)	\(3.3505\)	\(\Gamma_0(N)\)-optimal
42350.y3	42350f2	\([1, -1, 0, -617611792, 5907649709616]\)	\(941226862950447171561/45393906250000\)	\(1256532405471191406250000\)	\([2, 2]\)	\(14745600\)	\(3.6971\)
42350.y2	42350f3	\([1, -1, 0, -650221292, 5249166076116]\)	\(1098325674097093229481/205612182617187500\)	\(5691476935148239135742187500\)	\([2]\)	\(29491200\)	\(4.0437\)
42350.y1	42350f4	\([1, -1, 0, -9881674292, 378091360647116]\)	\(3855131356812007128171561/8967612500\)	\(248229258876757812500\)	\([2]\)	\(29491200\)	\(4.0437\)

Rank

The elliptic curves in class 42350f have rank \(0\).

Complex multiplication

The elliptic curves in class 42350f do not have complex multiplication.

Modular form 42350.2.a.f

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.