# Properties

 Label 71478.u Number of curves 4 Conductor 71478 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("71478.u1")

sage: E.isogeny_class()

## Elliptic curves in class 71478.u

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
71478.u1 71478ba3 [1, -1, 0, -261612, -51240560] [2] 663552
71478.u2 71478ba4 [1, -1, 0, -131652, -102262856] [2] 1327104
71478.u3 71478ba1 [1, -1, 0, -17937, 876649] [2] 221184 $$\Gamma_0(N)$$-optimal
71478.u4 71478ba2 [1, -1, 0, 14553, 3677287] [2] 442368

## Rank

sage: E.rank()

The elliptic curves in class 71478.u have rank $$0$$.

## Modular form 71478.2.a.u

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} + 2q^{7} - q^{8} + q^{11} + 4q^{13} - 2q^{14} + q^{16} + 6q^{17} + O(q^{20})$$

## 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.