# Properties

 Label 462.c Number of curves $4$ Conductor $462$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("c1")

sage: E.isogeny_class()

## Elliptic curves in class 462.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
462.c1 462b3 $$[1, 1, 0, -92004, 10703088]$$ $$86129359107301290313/9166294368$$ $$9166294368$$ $$$$ $$1920$$ $$1.3393$$
462.c2 462b2 $$[1, 1, 0, -5764, 164560]$$ $$21184262604460873/216872764416$$ $$216872764416$$ $$[2, 2]$$ $$960$$ $$0.99273$$
462.c3 462b4 $$[1, 1, 0, -1444, 410800]$$ $$-333345918055753/72923718045024$$ $$-72923718045024$$ $$$$ $$1920$$ $$1.3393$$
462.c4 462b1 $$[1, 1, 0, -644, -2352]$$ $$29609739866953/15259926528$$ $$15259926528$$ $$$$ $$480$$ $$0.64616$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 462.c have rank $$0$$.

## Complex multiplication

The elliptic curves in class 462.c do not have complex multiplication.

## Modular form462.2.a.c

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} + 2 q^{5} + q^{6} - q^{7} - q^{8} + q^{9} - 2 q^{10} + q^{11} - q^{12} + 2 q^{13} + q^{14} - 2 q^{15} + q^{16} + 6 q^{17} - q^{18} - 8 q^{19} + O(q^{20})$$

## Isogeny matrix

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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 