# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("l1")

sage: E.isogeny_class()

## Elliptic curves in class 30960.l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
30960.l1 30960c4 $$[0, 0, 0, -71643, -235942]$$ $$54477543627364/31494140625$$ $$23510250000000000$$ $$$$ $$147456$$ $$1.8308$$
30960.l2 30960c2 $$[0, 0, 0, -48423, 4087622]$$ $$67283921459536/260015625$$ $$48525156000000$$ $$[2, 2]$$ $$73728$$ $$1.4843$$
30960.l3 30960c1 $$[0, 0, 0, -48378, 4095623]$$ $$1073544204384256/16125$$ $$188082000$$ $$$$ $$36864$$ $$1.1377$$ $$\Gamma_0(N)$$-optimal
30960.l4 30960c3 $$[0, 0, 0, -25923, 7899122]$$ $$-2580786074884/34615360125$$ $$-25840227871872000$$ $$$$ $$147456$$ $$1.8308$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 30960.2.a.l

sage: E.q_eigenform(10)

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

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 