# Properties

 Label 4620a Number of curves $2$ Conductor $4620$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("a1")

sage: E.isogeny_class()

## Elliptic curves in class 4620a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4620.a2 4620a1 $$[0, -1, 0, -21, 126]$$ $$-67108864/343035$$ $$-5488560$$ $$$$ $$960$$ $$-0.022504$$ $$\Gamma_0(N)$$-optimal
4620.a1 4620a2 $$[0, -1, 0, -516, 4680]$$ $$59466754384/121275$$ $$31046400$$ $$$$ $$1920$$ $$0.32407$$

## Rank

sage: E.rank()

The elliptic curves in class 4620a have rank $$1$$.

## Complex multiplication

The elliptic curves in class 4620a do not have complex multiplication.

## Modular form4620.2.a.a

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} - q^{7} + q^{9} + q^{11} - 6q^{13} + q^{15} + 2q^{17} + O(q^{20})$$ ## 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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 