Elliptic curve isogeny class with LMFDB label 42978.r (Cremona label 42978v)

• Label: 42978.r
• Number of curves: $2$
• Conductor: $42978$
• CM: no
• Rank: $2$

Elliptic curves in class 42978.r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
42978.r1	42978v1	\([1, 0, 0, -803575, 284546441]\)	\(-57385609248046791394801/1784804944651399008\)	\(-1784804944651399008\)	\([5]\)	\(1800000\)	\(2.2789\)	\(\Gamma_0(N)\)-optimal
42978.r2	42978v2	\([1, 0, 0, 3910355, -13981592329]\)	\(6612600178387895114470319/88280159906925363790998\)	\(-88280159906925363790998\)	\([]\)	\(9000000\)	\(3.0837\)

Rank

The elliptic curves in class 42978.r have rank \(2\).

Complex multiplication

The elliptic curves in class 42978.r do not have complex multiplication.

Modular form 42978.2.a.r

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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.