Elliptic curve isogeny class with Cremona label 5415e (LMFDB label 5415.f)

• Label: 5415e
• Number of curves: $2$
• Conductor: $5415$
• CM: no
• Rank: $1$

Elliptic curves in class 5415e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
5415.f2	5415e1	$[0, -1, 1, -215, 1256]$	$3058794496/91125$	$32896125$	$[]$	$1296$	$0.21925$	$\Gamma_0(N)$-optimal
5415.f1	5415e2	$[0, -1, 1, -17315, 882761]$	$1590409933520896/45$	$16245$	$[]$	$3888$	$0.76855$

Rank

The elliptic curves in class 5415e have rank $1$.

Complex multiplication

The elliptic curves in class 5415e do not have complex multiplication.

Modular form 5415.2.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.

$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with Cremona labels.