# Properties

 Label 30960.g Number of curves $2$ Conductor $30960$ CM no Rank $2$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("g1")

sage: E.isogeny_class()

## Elliptic curves in class 30960.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
30960.g1 30960d1 $$[0, 0, 0, -2883, -47918]$$ $$3550014724/725625$$ $$541676160000$$ $$$$ $$36864$$ $$0.96701$$ $$\Gamma_0(N)$$-optimal
30960.g2 30960d2 $$[0, 0, 0, 6117, -287318]$$ $$16954370638/33698025$$ $$-50310881740800$$ $$$$ $$73728$$ $$1.3136$$

## Rank

sage: E.rank()

The elliptic curves in class 30960.g have rank $$2$$.

## Complex multiplication

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

## Modular form 30960.2.a.g

sage: E.q_eigenform(10)

$$q - q^{5} - 2q^{7} - 4q^{11} - 6q^{13} - 2q^{17} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 