# Properties

 Label 3150.f Number of curves 8 Conductor 3150 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("3150.f1")

sage: E.isogeny_class()

## Elliptic curves in class 3150.f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3150.f1 3150k7 [1, -1, 0, -79027317, 270424292341] [2] 221184
3150.f2 3150k6 [1, -1, 0, -4939317, 4226108341] [2, 2] 110592
3150.f3 3150k8 [1, -1, 0, -4579317, 4867988341] [2] 221184
3150.f4 3150k4 [1, -1, 0, -980442, 367339216] [2] 73728
3150.f5 3150k3 [1, -1, 0, -331317, 55868341] [2] 55296
3150.f6 3150k2 [1, -1, 0, -129942, -9432284] [2, 2] 36864
3150.f7 3150k1 [1, -1, 0, -111942, -14382284] [2] 18432 $$\Gamma_0(N)$$-optimal
3150.f8 3150k5 [1, -1, 0, 432558, -69619784] [2] 73728

## Rank

sage: E.rank()

The elliptic curves in class 3150.f have rank $$0$$.

## Modular form3150.2.a.f

sage: E.q_eigenform(10)

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

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.