Properties

 Label 229320.ds Number of curves $4$ Conductor $229320$ CM no Rank $1$ Graph

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Show commands: SageMath
sage: E = EllipticCurve("ds1")

sage: E.isogeny_class()

Elliptic curves in class 229320.ds

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
229320.ds1 229320o4 $$[0, 0, 0, -247665747, -1500192649186]$$ $$19129597231400697604/26325$$ $$2311980170572800$$ $$[2]$$ $$14155776$$ $$3.1144$$
229320.ds2 229320o2 $$[0, 0, 0, -15479247, -23440071886]$$ $$18681746265374416/693005625$$ $$15215719497582240000$$ $$[2, 2]$$ $$7077888$$ $$2.7678$$
229320.ds3 229320o3 $$[0, 0, 0, -14764827, -25701496954]$$ $$-4053153720264484/903687890625$$ $$-79365944292944400000000$$ $$[2]$$ $$14155776$$ $$3.1144$$
229320.ds4 229320o1 $$[0, 0, 0, -1012242, -330478099]$$ $$83587439220736/13990184325$$ $$19198141466084053200$$ $$[2]$$ $$3538944$$ $$2.4212$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 229320.ds have rank $$1$$.

Complex multiplication

The elliptic curves in class 229320.ds do not have complex multiplication.

Modular form 229320.2.a.ds

sage: E.q_eigenform(10)

$$q + q^{5} - q^{13} + 2 q^{17} + O(q^{20})$$

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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with LMFDB labels.