# Properties

 Label 50820e Number of curves $2$ Conductor $50820$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("e1")

sage: E.isogeny_class()

## Elliptic curves in class 50820e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
50820.e2 50820e1 $$[0, -1, 0, -2581, -157430]$$ $$-67108864/343035$$ $$-9723318842160$$ $$$$ $$115200$$ $$1.1764$$ $$\Gamma_0(N)$$-optimal
50820.e1 50820e2 $$[0, -1, 0, -62476, -5979224]$$ $$59466754384/121275$$ $$55000591430400$$ $$$$ $$230400$$ $$1.5230$$

## Rank

sage: E.rank()

The elliptic curves in class 50820e have rank $$0$$.

## Complex multiplication

The elliptic curves in class 50820e do not have complex multiplication.

## Modular form 50820.2.a.e

sage: E.q_eigenform(10)

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