# Properties

 Label 28611.z Number of curves 3 Conductor 28611 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("28611.z1")

sage: E.isogeny_class()

## Elliptic curves in class 28611.z

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
28611.z1 28611w3 [0, 0, 1, -20340687, 35309904183] [] 768000
28611.z2 28611w2 [0, 0, 1, -26877, 3071853] [] 153600
28611.z3 28611w1 [0, 0, 1, -867, -23337] [] 30720 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 28611.z have rank $$1$$.

## Modular form 28611.2.a.z

sage: E.q_eigenform(10)

$$q + 2q^{2} + 2q^{4} + q^{5} + 2q^{7} + 2q^{10} + q^{11} + 4q^{13} + 4q^{14} - 4q^{16} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 