# Properties

 Label 3150.z Number of curves 2 Conductor 3150 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("3150.z1")

sage: E.isogeny_class()

## Elliptic curves in class 3150.z

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3150.z1 3150z2 [1, -1, 1, -20465, 1131937]  6144
3150.z2 3150z1 [1, -1, 1, -1265, 18337]  3072 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 3150.z have rank $$1$$.

## Modular form3150.2.a.z

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 