LMFDB - Elliptic curve isogeny class with LMFDB label 435600.in (Cremona label 435600in)

Properties

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Show commands: SageMath

sage:E = EllipticCurve("in1") E.isogeny_class()

Rank

sage:E.rank()

The elliptic curves in class 435600.in have rank $0$.

The elliptic curves in class 435600.in 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.

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

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

The vertices are labelled with LMFDB labels.

sage:E.isogeny_class().curves

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
435600.in1	435600in1	$[0, 0, 0, -2187075, 1265085250]$	$-1693700041/32000$	$-21858895872000000000$	$[]$	$9953280$	$2.5056$	$\Gamma_0(N)$-optimal
435600.in2	435600in2	$[0, 0, 0, 8702925, 5915115250]$	$106718863559/83886080$	$-57301783994695680000000$	$[]$	$29859840$	$3.0549$

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Classical	Maass
Hilbert	Bianchi

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
435600.in1	435600in1	\([0, 0, 0, -2187075, 1265085250]\)	\(-1693700041/32000\)	\(-21858895872000000000\)	\([]\)	\(9953280\)	\(2.5056\)	\(\Gamma_0(N)\)-optimal
435600.in2	435600in2	\([0, 0, 0, 8702925, 5915115250]\)	\(106718863559/83886080\)	\(-57301783994695680000000\)	\([]\)	\(29859840\)	\(3.0549\)