Elliptic curve isogeny class with Cremona label 21675i (LMFDB label 21675.a)

• Label: 21675i
• Number of curves: $2$
• Conductor: $21675$
• CM: no
• Rank: $1$

Elliptic curves in class 21675i

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
21675.a2	21675i1	\([0, -1, 1, 482, 17808]\)	\(20480/243\)	\(-146635731675\)	\([]\)	\(30720\)	\(0.82351\)	\(\Gamma_0(N)\)-optimal
21675.a1	21675i2	\([0, -1, 1, -60208, -5808432]\)	\(-102400/3\)	\(-707155341796875\)	\([]\)	\(153600\)	\(1.6282\)

Rank

The elliptic curves in class 21675i have rank \(1\).

Complex multiplication

The elliptic curves in class 21675i do not have complex multiplication.

Modular form 21675.2.a.i

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.