# Properties

 Label 700.d Number of curves $2$ Conductor $700$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 700.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
700.d1 700a2 $$[0, -1, 0, -20133, -1092863]$$ $$-225637236736/1715$$ $$-6860000000$$ $$[]$$ $$864$$ $$1.0623$$
700.d2 700a1 $$[0, -1, 0, -133, -2863]$$ $$-65536/875$$ $$-3500000000$$ $$[]$$ $$288$$ $$0.51296$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 700.d have rank $$0$$.

## Complex multiplication

The elliptic curves in class 700.d do not have complex multiplication.

## Modular form700.2.a.d

sage: E.q_eigenform(10)

$$q - q^{3} - q^{7} - 2q^{9} + 3q^{11} + q^{13} + 3q^{17} + 2q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 