# Properties

 Label 70805.bd Number of curves $3$ Conductor $70805$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bd1")

sage: E.isogeny_class()

## Elliptic curves in class 70805.bd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
70805.bd1 70805e3 $$[0, 1, 1, -1859811, 1020602020]$$ $$-250523582464/13671875$$ $$-38824855443294921875$$ $$[]$$ $$1451520$$ $$2.5170$$
70805.bd2 70805e1 $$[0, 1, 1, -18881, -1114130]$$ $$-262144/35$$ $$-99391629934835$$ $$[]$$ $$161280$$ $$1.4184$$ $$\Gamma_0(N)$$-optimal
70805.bd3 70805e2 $$[0, 1, 1, 122729, 2865111]$$ $$71991296/42875$$ $$-121754746670172875$$ $$[]$$ $$483840$$ $$1.9677$$

## Rank

sage: E.rank()

The elliptic curves in class 70805.bd have rank $$0$$.

## Complex multiplication

The elliptic curves in class 70805.bd do not have complex multiplication.

## Modular form 70805.2.a.bd

sage: E.q_eigenform(10)

$$q + q^{3} - 2q^{4} - q^{5} - 2q^{9} + 3q^{11} - 2q^{12} - 5q^{13} - q^{15} + 4q^{16} - 2q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 