# Properties

 Label 32912.y Number of curves 4 Conductor 32912 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("32912.y1")

sage: E.isogeny_class()

## Elliptic curves in class 32912.y

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
32912.y1 32912bb4 [0, -1, 0, -218808, -27150352]  311040
32912.y2 32912bb3 [0, -1, 0, -199448, -34212880]  155520
32912.y3 32912bb2 [0, -1, 0, -83288, 9277424]  103680
32912.y4 32912bb1 [0, -1, 0, -5848, 108528]  51840 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 32912.y have rank $$0$$.

## Modular form 32912.2.a.y

sage: E.q_eigenform(10)

$$q + 2q^{3} - 4q^{7} + q^{9} - 2q^{13} + q^{17} - 4q^{19} + O(q^{20})$$

## 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. 