# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("215600.hf1")

sage: E.isogeny_class()

## Elliptic curves in class 215600.hf

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
215600.hf1 215600es4 [0, -1, 0, -511874008, -4331034889488]  95551488
215600.hf2 215600es2 [0, -1, 0, -70090008, 223873398512]  31850496
215600.hf3 215600es1 [0, -1, 0, -1098008, 8618358512]  15925248 $$\Gamma_0(N)$$-optimal
215600.hf4 215600es3 [0, -1, 0, 9877992, -232151177488]  47775744

## Rank

sage: E.rank()

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

## Modular form 215600.2.a.hf

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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 