# Properties

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

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

sage: E.isogeny_class()

## Elliptic curves in class 93600h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
93600.n2 93600h1 $$[0, 0, 0, 675, 121500]$$ $$1728/325$$ $$-6396975000000$$ $$$$ $$147456$$ $$1.1365$$ $$\Gamma_0(N)$$-optimal
93600.n1 93600h2 $$[0, 0, 0, -33075, 2247750]$$ $$25412184/845$$ $$133057080000000$$ $$$$ $$294912$$ $$1.4831$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 93600.2.a.h

sage: E.q_eigenform(10)

$$q - 4q^{7} + 4q^{11} + q^{13} + 2q^{17} - 4q^{19} + O(q^{20})$$ ## 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. 