# Properties

 Label 4800.ca Number of curves $4$ Conductor $4800$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("ca1")

sage: E.isogeny_class()

## Elliptic curves in class 4800.ca

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4800.ca1 4800cc3 $$[0, 1, 0, -5633, -163137]$$ $$38614472/405$$ $$207360000000$$ $$$$ $$6144$$ $$0.98802$$
4800.ca2 4800cc2 $$[0, 1, 0, -633, 1863]$$ $$438976/225$$ $$14400000000$$ $$[2, 2]$$ $$3072$$ $$0.64145$$
4800.ca3 4800cc1 $$[0, 1, 0, -508, 4238]$$ $$14526784/15$$ $$15000000$$ $$$$ $$1536$$ $$0.29488$$ $$\Gamma_0(N)$$-optimal
4800.ca4 4800cc4 $$[0, 1, 0, 2367, 16863]$$ $$2863288/1875$$ $$-960000000000$$ $$$$ $$6144$$ $$0.98802$$

## Rank

sage: E.rank()

The elliptic curves in class 4800.ca have rank $$1$$.

## Complex multiplication

The elliptic curves in class 4800.ca do not have complex multiplication.

## Modular form4800.2.a.ca

sage: E.q_eigenform(10)

$$q + q^{3} + q^{9} - 4q^{11} + 2q^{13} + 2q^{17} - 8q^{19} + O(q^{20})$$ ## 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. 