# Properties

 Label 215600er Number of curves $4$ Conductor $215600$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("er1")

sage: E.isogeny_class()

## Elliptic curves in class 215600er

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
215600.he4 215600er1 $$[0, -1, 0, -55533, 4952312]$$ $$643956736/15125$$ $$444860281250000$$ $$$$ $$995328$$ $$1.5962$$ $$\Gamma_0(N)$$-optimal
215600.he3 215600er2 $$[0, -1, 0, -122908, -9331188]$$ $$436334416/171875$$ $$80883687500000000$$ $$$$ $$1990656$$ $$1.9428$$
215600.he2 215600er3 $$[0, -1, 0, -545533, -152950188]$$ $$610462990336/8857805$$ $$260527975111250000$$ $$$$ $$2985984$$ $$2.1455$$
215600.he1 215600er4 $$[0, -1, 0, -8697908, -9870581188]$$ $$154639330142416/33275$$ $$15659081900000000$$ $$$$ $$5971968$$ $$2.4921$$

## Rank

sage: E.rank()

The elliptic curves in class 215600er have rank $$0$$.

## Complex multiplication

The elliptic curves in class 215600er do not have complex multiplication.

## Modular form 215600.2.a.er

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 