# Properties

 Label 3150w Number of curves $4$ Conductor $3150$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("3150.bb1")

sage: E.isogeny_class()

## Elliptic curves in class 3150w

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3150.bb2 3150w1 [1, -1, 1, -2630, 52497]  2304 $$\Gamma_0(N)$$-optimal
3150.bb3 3150w2 [1, -1, 1, -1880, 82497]  4608
3150.bb1 3150w3 [1, -1, 1, -10505, -360503]  6912
3150.bb4 3150w4 [1, -1, 1, 16495, -1926503]  13824

## Rank

sage: E.rank()

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

## Modular form3150.2.a.bb

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 