# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("3150.bj1")

sage: E.isogeny_class()

## Elliptic curves in class 3150bm

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3150.bj4 3150bm1 [1, -1, 1, 520, 7147]  3072 $$\Gamma_0(N)$$-optimal
3150.bj3 3150bm2 [1, -1, 1, -3980, 79147] [2, 2] 6144
3150.bj2 3150bm3 [1, -1, 1, -19730, -991853]  12288
3150.bj1 3150bm4 [1, -1, 1, -60230, 5704147]  12288

## Rank

sage: E.rank()

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

## Modular form3150.2.a.bj

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + q^{7} + q^{8} - 4q^{11} + 6q^{13} + q^{14} + q^{16} + 2q^{17} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 