# Properties

 Label 102c Number of curves $4$ Conductor $102$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("102.b1")

sage: E.isogeny_class()

## Elliptic curves in class 102c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
102.b2 102c1 [1, 0, 1, -256, 1550]  24 $$\Gamma_0(N)$$-optimal
102.b3 102c2 [1, 0, 1, -216, 2062]  48
102.b1 102c3 [1, 0, 1, -751, -6046]  72
102.b4 102c4 [1, 0, 1, 1809, -37790]  144

## Rank

sage: E.rank()

The elliptic curves in class 102c have rank $$0$$.

## Modular form102.2.a.b

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} - q^{6} + 2q^{7} - q^{8} + q^{9} + q^{12} + 2q^{13} - 2q^{14} + q^{16} - q^{17} - q^{18} - 4q^{19} + O(q^{20})$$

## 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. 