# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("he1")

sage: E.isogeny_class()

## Elliptic curves in class 215600.he

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
215600.he1 215600er4 [0, -1, 0, -8697908, -9870581188]  5971968
215600.he2 215600er3 [0, -1, 0, -545533, -152950188]  2985984
215600.he3 215600er2 [0, -1, 0, -122908, -9331188]  1990656
215600.he4 215600er1 [0, -1, 0, -55533, 4952312]  995328 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 215600.2.a.he

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 LMFDB 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 LMFDB labels. 