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SageMath
E = EllipticCurve("dy1")
E.isogeny_class()
Elliptic curves in class 363090dy
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 363090.dy4 | 363090dy1 | \([1, 0, 1, -3391708, 681185306]\) | \(36676733979624816169/19519718400000000\) | \(2296475350041600000000\) | \([2]\) | \(28311552\) | \(2.7902\) | \(\Gamma_0(N)\)-optimal |
| 363090.dy2 | 363090dy2 | \([1, 0, 1, -42591708, 106866145306]\) | \(72629093972969564016169/93022316019360000\) | \(10943982457361684640000\) | \([2, 2]\) | \(56623104\) | \(3.1368\) | |
| 363090.dy1 | 363090dy3 | \([1, 0, 1, -681257708, 6844026046106]\) | \(297214339265273649756432169/488484917902800\) | \(57469762106346517200\) | \([2]\) | \(113246208\) | \(3.4833\) | |
| 363090.dy3 | 363090dy4 | \([1, 0, 1, -31125708, 165700484506]\) | \(-28346090452899214800169/84418326220247182800\) | \(-9931731661485860809237200\) | \([2]\) | \(113246208\) | \(3.4833\) |
Rank
sage: E.rank()
The elliptic curves in class 363090dy have rank \(0\).
Complex multiplication
The elliptic curves in class 363090dy do not have complex multiplication.Modular form 363090.2.a.dy
sage: E.q_eigenform(10)
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 Cremona 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 Cremona labels.
