Elliptic curve isogeny class with LMFDB label 1305.f (Cremona label 1305g)

• Label: 1305.f
• Number of curves: $2$
• Conductor: $1305$
• CM: no
• Rank: $0$

Elliptic curves in class 1305.f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1305.f1	1305g1	$[1, -1, 0, -24, -37]$	$2146689/145$	$105705$	$[2]$	$128$	$-0.28720$	$\Gamma_0(N)$-optimal
1305.f2	1305g2	$[1, -1, 0, 21, -190]$	$1367631/21025$	$-15327225$	$[2]$	$256$	$0.059378$

Rank

The elliptic curves in class 1305.f have rank $0$.

Complex multiplication

The elliptic curves in class 1305.f do not have complex multiplication.

Modular form 1305.2.a.f

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.

$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with LMFDB labels.