# Properties

 Label 10920.e Number of curves $2$ Conductor $10920$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("e1")

sage: E.isogeny_class()

## Elliptic curves in class 10920.e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10920.e1 10920l1 $$[0, -1, 0, -19656, -492804]$$ $$820221748268836/369468094905$$ $$378335329182720$$ $$$$ $$37632$$ $$1.4925$$ $$\Gamma_0(N)$$-optimal
10920.e2 10920l2 $$[0, -1, 0, 68224, -3761940]$$ $$17147425715207422/12872524043925$$ $$-26362929241958400$$ $$$$ $$75264$$ $$1.8391$$

## Rank

sage: E.rank()

The elliptic curves in class 10920.e have rank $$0$$.

## Complex multiplication

The elliptic curves in class 10920.e do not have complex multiplication.

## Modular form 10920.2.a.e

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} + q^{7} + q^{9} + 2q^{11} + q^{13} + q^{15} - 2q^{17} - 6q^{19} + O(q^{20})$$ ## 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. 