Elliptic curve isogeny class with Cremona label 212415t (LMFDB label 212415.w)

• Label: 212415t
• Number of curves: $4$
• Conductor: $212415$
• CM: no
• Rank: $1$

Elliptic curves in class 212415t

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
212415.w4	212415t1	\([1, 0, 0, 197959, -57000000]\)	\(302111711/669375\)	\(-1900864922503719375\)	\([2]\)	\(3538944\)	\(2.1916\)	\(\Gamma_0(N)\)-optimal
212415.w3	212415t2	\([1, 0, 0, -1572166, -622377925]\)	\(151334226289/28676025\)	\(81433053280059338025\)	\([2, 2]\)	\(7077888\)	\(2.5381\)
212415.w2	212415t3	\([1, 0, 0, -7590591, 7482033180]\)	\(17032120495489/1339001685\)	\(3802444570218300148485\)	\([2]\)	\(14155776\)	\(2.8847\)
212415.w1	212415t4	\([1, 0, 0, -23875741, -44903895730]\)	\(530044731605089/26309115\)	\(74711594914086186315\)	\([2]\)	\(14155776\)	\(2.8847\)

Rank

The elliptic curves in class 212415t have rank \(1\).

Complex multiplication

The elliptic curves in class 212415t do not have complex multiplication.

Modular form 212415.2.a.t

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.