# Properties

 Label 60984v Number of curves $2$ Conductor $60984$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("v1")

sage: E.isogeny_class()

## Elliptic curves in class 60984v

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
60984.i2 60984v1 $$[0, 0, 0, 4168329, 3472374026]$$ $$24226243449392/29774625727$$ $$-9843961706338262646528$$ $$$$ $$2764800$$ $$2.9062$$ $$\Gamma_0(N)$$-optimal
60984.i1 60984v2 $$[0, 0, 0, -24820851, 33383409950]$$ $$1278763167594532/375974556419$$ $$497212515096700767243264$$ $$$$ $$5529600$$ $$3.2528$$

## Rank

sage: E.rank()

The elliptic curves in class 60984v have rank $$1$$.

## Complex multiplication

The elliptic curves in class 60984v do not have complex multiplication.

## Modular form 60984.2.a.v

sage: E.q_eigenform(10)

$$q - 2q^{5} - q^{7} + 4q^{17} - 4q^{19} + O(q^{20})$$ ## 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 Cremona 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 Cremona labels. 