# Properties

 Label 2960.m Number of curves $4$ Conductor $2960$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("m1")

sage: E.isogeny_class()

## Elliptic curves in class 2960.m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2960.m1 2960n3 $$[0, -1, 0, -84400, 9465792]$$ $$16232905099479601/4052240$$ $$16597975040$$ $$$$ $$6912$$ $$1.3367$$
2960.m2 2960n4 $$[0, -1, 0, -84080, 9540800]$$ $$-16048965315233521/256572640900$$ $$-1050921537126400$$ $$$$ $$13824$$ $$1.6832$$
2960.m3 2960n1 $$[0, -1, 0, -1200, 9152]$$ $$46694890801/18944000$$ $$77594624000$$ $$$$ $$2304$$ $$0.78735$$ $$\Gamma_0(N)$$-optimal
2960.m4 2960n2 $$[0, -1, 0, 3920, 62400]$$ $$1625964918479/1369000000$$ $$-5607424000000$$ $$$$ $$4608$$ $$1.1339$$

## Rank

sage: E.rank()

The elliptic curves in class 2960.m have rank $$0$$.

## Complex multiplication

The elliptic curves in class 2960.m do not have complex multiplication.

## Modular form2960.2.a.m

sage: E.q_eigenform(10)

$$q + 2q^{3} + q^{5} - 2q^{7} + q^{9} + 2q^{13} + 2q^{15} + 6q^{17} - 2q^{19} + O(q^{20})$$ ## 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 LMFDB 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 LMFDB labels. 