Elliptic curve isogeny class with Cremona label 397800e (LMFDB label 397800.e)

• Label: 397800e
• Number of curves: $4$
• Conductor: $397800$
• CM: no
• Rank: $0$

Elliptic curves in class 397800e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
397800.e4	397800e1	\([0, 0, 0, -11150175, 3977649250]\)	\(52575237512036944/28081530070425\)	\(81885741685359300000000\)	\([2]\)	\(34603008\)	\(3.0879\)	\(\Gamma_0(N)\)-optimal
397800.e2	397800e2	\([0, 0, 0, -139674675, 634647370750]\)	\(25836234020391349156/33847087730625\)	\(394792431290010000000000\)	\([2, 2]\)	\(69206016\)	\(3.4345\)
397800.e1	397800e3	\([0, 0, 0, -2234091675, 40644295321750]\)	\(52862679907533400952738/90903515625\)	\(2120597212500000000000\)	\([2]\)	\(138412032\)	\(3.7811\)
397800.e3	397800e4	\([0, 0, 0, -101649675, 987861595750]\)	\(-4979252943420552578/15190164405108225\)	\(-354356155242364672800000000\)	\([2]\)	\(138412032\)	\(3.7811\)

Rank

The elliptic curves in class 397800e have rank \(0\).

Complex multiplication

The elliptic curves in class 397800e do not have complex multiplication.

Modular form 397800.2.a.e

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.