# Properties

 Label 350658.di Number of curves $2$ Conductor $350658$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("di1")

sage: E.isogeny_class()

## Elliptic curves in class 350658.di

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
350658.di1 350658di2 $$[1, -1, 1, -144414590, -667945834531]$$ $$3776104682692733708238625/3408048$$ $$300620506032$$ $$[]$$ $$19906560$$ $$2.8825$$
350658.di2 350658di1 $$[1, -1, 1, -1783310, -915406819]$$ $$7110352307247726625/6866458324992$$ $$605683422389219328$$ $$[]$$ $$6635520$$ $$2.3332$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 350658.di have rank $$0$$.

## Complex multiplication

The elliptic curves in class 350658.di do not have complex multiplication.

## Modular form 350658.2.a.di

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} - q^{7} + q^{8} - 2q^{13} - q^{14} + q^{16} + 6q^{17} - 2q^{19} + O(q^{20})$$ ## 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. 