# Properties

 Label 93600.er Number of curves $2$ Conductor $93600$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("er1")

sage: E.isogeny_class()

## Elliptic curves in class 93600.er

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
93600.er1 93600cm2 $$[0, 0, 0, -55875, -1656250]$$ $$26463592/13689$$ $$9979281000000000$$ $$[2]$$ $$573440$$ $$1.7620$$
93600.er2 93600cm1 $$[0, 0, 0, -44625, -3625000]$$ $$107850176/117$$ $$10661625000000$$ $$[2]$$ $$286720$$ $$1.4154$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 93600.er have rank $$0$$.

## Complex multiplication

The elliptic curves in class 93600.er do not have complex multiplication.

## Modular form 93600.2.a.er

sage: E.q_eigenform(10)

$$q + 4q^{7} - 2q^{11} + q^{13} - 2q^{19} + O(q^{20})$$

## 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.