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SageMath
E = EllipticCurve("da1")
E.isogeny_class()
Elliptic curves in class 254898da
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 254898.da4 | 254898da1 | \([1, -1, 0, 124794, 4584917812]\) | \(103823/4386816\) | \(-9081523591611753590784\) | \([2]\) | \(21233664\) | \(2.8923\) | \(\Gamma_0(N)\)-optimal |
| 254898.da3 | 254898da2 | \([1, -1, 0, -40658886, 98020328692]\) | \(3590714269297/73410624\) | \(151973621353377938995776\) | \([2, 2]\) | \(42467328\) | \(3.2388\) | |
| 254898.da1 | 254898da3 | \([1, -1, 0, -647316126, 6339188682364]\) | \(14489843500598257/6246072\) | \(12930528707587828843128\) | \([2]\) | \(84934656\) | \(3.5854\) | |
| 254898.da2 | 254898da4 | \([1, -1, 0, -86540526, -163771132820]\) | \(34623662831857/14438442312\) | \(29890256277572013807210888\) | \([2]\) | \(84934656\) | \(3.5854\) |
Rank
sage: E.rank()
The elliptic curves in class 254898da have rank \(1\).
Complex multiplication
The elliptic curves in class 254898da do not have complex multiplication.Modular form 254898.2.a.da
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.
