# Properties

 Label 93600cn Number of curves $2$ Conductor $93600$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("cn1")

sage: E.isogeny_class()

## Elliptic curves in class 93600cn

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
93600.m2 93600cn1 $$[0, 0, 0, -44625, 3625000]$$ $$107850176/117$$ $$10661625000000$$ $$$$ $$286720$$ $$1.4154$$ $$\Gamma_0(N)$$-optimal
93600.m1 93600cn2 $$[0, 0, 0, -55875, 1656250]$$ $$26463592/13689$$ $$9979281000000000$$ $$$$ $$573440$$ $$1.7620$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 93600.2.a.cn

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 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. 