# Properties

 Label 3150bf Number of curves $8$ Conductor $3150$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("3150.ba1")

sage: E.isogeny_class()

## Elliptic curves in class 3150bf

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3150.ba7 3150bf1 [1, -1, 1, -9230, 122397] [4] 9216 $$\Gamma_0(N)$$-optimal
3150.ba5 3150bf2 [1, -1, 1, -81230, -8805603] [2, 2] 18432
3150.ba4 3150bf3 [1, -1, 1, -603230, 180482397] [4] 27648
3150.ba2 3150bf4 [1, -1, 1, -1296230, -567705603] [2] 36864
3150.ba6 3150bf5 [1, -1, 1, -18230, -22161603] [2] 36864
3150.ba3 3150bf6 [1, -1, 1, -607730, 177656397] [2, 2] 55296
3150.ba1 3150bf7 [1, -1, 1, -1451480, -423093603] [2] 110592
3150.ba8 3150bf8 [1, -1, 1, 164020, 597488397] [2] 110592

## Rank

sage: E.rank()

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

## Modular form3150.2.a.ba

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.