# Properties

 Label 30960.bp Number of curves $4$ Conductor $30960$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("bp1")

sage: E.isogeny_class()

## Elliptic curves in class 30960.bp

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
30960.bp1 30960bt4 $$[0, 0, 0, -99147, 12016186]$$ $$36097320816649/80625$$ $$240744960000$$ $$$$ $$90112$$ $$1.4291$$
30960.bp2 30960bt3 $$[0, 0, 0, -17067, -618086]$$ $$184122897769/51282015$$ $$153127276277760$$ $$$$ $$90112$$ $$1.4291$$
30960.bp3 30960bt2 $$[0, 0, 0, -6267, 183274]$$ $$9116230969/416025$$ $$1242243993600$$ $$[2, 2]$$ $$45056$$ $$1.0825$$
30960.bp4 30960bt1 $$[0, 0, 0, 213, 10906]$$ $$357911/17415$$ $$-52000911360$$ $$$$ $$22528$$ $$0.73595$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 30960.bp have rank $$0$$.

## Complex multiplication

The elliptic curves in class 30960.bp do not have complex multiplication.

## Modular form 30960.2.a.bp

sage: E.q_eigenform(10)

$$q + q^{5} + 4q^{11} + 6q^{13} + 2q^{17} + O(q^{20})$$ ## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 