# Properties

 Label 630i Number of curves 8 Conductor 630 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("630.h1")
sage: E.isogeny_class()

## Elliptic curves in class 630i

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
630.h7 630i1 [1, -1, 1, -4478, -114163] 2 768 $$\Gamma_0(N)$$-optimal
630.h6 630i2 [1, -1, 1, -5198, -74419] 4 1536
630.h5 630i3 [1, -1, 1, -13253, 449597] 6 2304
630.h4 630i4 [1, -1, 1, -39218, 2946557] 2 3072
630.h8 630i5 [1, -1, 1, 17302, -560419] 2 3072
630.h2 630i6 [1, -1, 1, -197573, 33848381] 12 4608
630.h1 630i7 [1, -1, 1, -3161093, 2164026557] 6 9216
630.h3 630i8 [1, -1, 1, -183173, 38980541] 6 9216

## Rank

sage: E.rank()

The elliptic curves in class 630i have rank $$0$$.

## Modular form630.2.a.h

sage: E.q_eigenform(10)
$$q + q^{2} + q^{4} - q^{5} + q^{7} + q^{8} - q^{10} + 2q^{13} + q^{14} + q^{16} + 6q^{17} + 8q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.