# Properties

 Label 93600.d Number of curves $2$ Conductor $93600$ CM no Rank $2$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("d1")

sage: E.isogeny_class()

## Elliptic curves in class 93600.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
93600.d1 93600eq1 $$[0, 0, 0, -19425, 1042000]$$ $$1111934656/65$$ $$47385000000$$ $$$$ $$221184$$ $$1.1111$$ $$\Gamma_0(N)$$-optimal
93600.d2 93600eq2 $$[0, 0, 0, -18300, 1168000]$$ $$-14526784/4225$$ $$-197121600000000$$ $$$$ $$442368$$ $$1.4577$$

## Rank

sage: E.rank()

The elliptic curves in class 93600.d have rank $$2$$.

## Complex multiplication

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

## Modular form 93600.2.a.d

sage: E.q_eigenform(10)

$$q - 4q^{7} - 6q^{11} + q^{13} - 6q^{17} + 6q^{19} + O(q^{20})$$ ## 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. 