Elliptic curve isogeny class with Cremona label 234234m (LMFDB label 234234.m)

• Label: 234234m
• Number of curves: $4$
• Conductor: $234234$
• CM: no
• Rank: $1$

Elliptic curves in class 234234m

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
234234.m4	234234m1	\([1, -1, 0, 5292, 88960]\)	\(4657463/3696\)	\(-13005276940656\)	\([2]\)	\(589824\)	\(1.2043\)	\(\Gamma_0(N)\)-optimal
234234.m3	234234m2	\([1, -1, 0, -25128, 788620]\)	\(498677257/213444\)	\(751054743322884\)	\([2, 2]\)	\(1179648\)	\(1.5509\)
234234.m1	234234m3	\([1, -1, 0, -344538, 77894194]\)	\(1285429208617/614922\)	\(2163752951001642\)	\([2]\)	\(2359296\)	\(1.8974\)
234234.m2	234234m4	\([1, -1, 0, -192438, -31903754]\)	\(223980311017/4278582\)	\(15055233718426902\)	\([2]\)	\(2359296\)	\(1.8974\)

Rank

The elliptic curves in class 234234m have rank \(1\).

Complex multiplication

The elliptic curves in class 234234m do not have complex multiplication.

Modular form 234234.2.a.m

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.