LMFDB - Elliptic curve isogeny class with LMFDB label 8664.c (Cremona label 8664a)

Properties

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Show commands: SageMath

sage:E = EllipticCurve("c1") E.isogeny_class()

Elliptic curves in class 8664.c

sage:E.isogeny_class().curves

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
8664.c1	8664a2	$[0, -1, 0, -424, 3484]$	$1203052/9$	$63212544$	$[2]$	$3200$	$0.32709$
8664.c2	8664a1	$[0, -1, 0, -44, -12]$	$5488/3$	$5267712$	$[2]$	$1600$	$-0.019479$	$\Gamma_0(N)$-optimal

sage:E.rank()

The elliptic curves in class 8664.c have rank $1$.

The elliptic curves in class 8664.c do not have complex multiplication.

sage:E.q_eigenform(10)

sage:E.isogeny_class().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.

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

sage:E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels.

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Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
8664.c1	8664a2	\([0, -1, 0, -424, 3484]\)	\(1203052/9\)	\(63212544\)	\([2]\)	\(3200\)	\(0.32709\)
8664.c2	8664a1	\([0, -1, 0, -44, -12]\)	\(5488/3\)	\(5267712\)	\([2]\)	\(1600\)	\(-0.019479\)	\(\Gamma_0(N)\)-optimal