# Properties

 Label 700.f Number of curves $2$ Conductor $700$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("f1")

sage: E.isogeny_class()

## Elliptic curves in class 700.f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
700.f1 700e1 $$[0, 0, 0, -2000, -34375]$$ $$28311552/49$$ $$1531250000$$ $$$$ $$360$$ $$0.65639$$ $$\Gamma_0(N)$$-optimal
700.f2 700e2 $$[0, 0, 0, -1375, -56250]$$ $$-574992/2401$$ $$-1200500000000$$ $$$$ $$720$$ $$1.0030$$

## Rank

sage: E.rank()

The elliptic curves in class 700.f have rank $$1$$.

## Complex multiplication

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

## Modular form700.2.a.f

sage: E.q_eigenform(10)

$$q - q^{7} - 3q^{9} - 4q^{13} - 4q^{17} + 4q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 