# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("h1")

sage: E.isogeny_class()

## Elliptic curves in class 60984.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
60984.h1 60984w2 $$[0, 0, 0, -253011, -48967490]$$ $$1354435492/539$$ $$712807664937984$$ $$$$ $$368640$$ $$1.8140$$
60984.h2 60984w1 $$[0, 0, 0, -13431, -1003574]$$ $$-810448/847$$ $$-280031582654208$$ $$$$ $$184320$$ $$1.4674$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 60984.2.a.h

sage: E.q_eigenform(10)

$$q - 2q^{5} - q^{7} - 4q^{13} + 4q^{19} + O(q^{20})$$ ## 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 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. 