# Properties

 Label 100800.if Number of curves $2$ Conductor $100800$ CM no Rank $0$ Graph # Learn more

Show commands: SageMath
sage: E = EllipticCurve("if1")

sage: E.isogeny_class()

## Elliptic curves in class 100800.if

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
100800.if1 100800of2 $$[0, 0, 0, -5047500, -4618150000]$$ $$-7620530425/526848$$ $$-983224811520000000000$$ $$[]$$ $$4976640$$ $$2.7791$$
100800.if2 100800of1 $$[0, 0, 0, 352500, -6550000]$$ $$2595575/1512$$ $$-2821754880000000000$$ $$[]$$ $$1658880$$ $$2.2298$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 100800.if have rank $$0$$.

## Complex multiplication

The elliptic curves in class 100800.if do not have complex multiplication.

## Modular form 100800.2.a.if

sage: E.q_eigenform(10)

$$q + q^{7} - 6q^{11} - q^{13} + 3q^{17} - 4q^{19} + O(q^{20})$$ ## 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 LMFDB numbering.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels. 