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SageMath
E = EllipticCurve("cy1")
E.isogeny_class()
Elliptic curves in class 388815.cy
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 388815.cy1 | 388815cy3 | \([1, 1, 0, -111292353, 451857539988]\) | \(8753151307882969/65205\) | \(1135628166054982005\) | \([2]\) | \(35684352\) | \(3.0590\) | |
| 388815.cy2 | 388815cy2 | \([1, 1, 0, -6960328, 7048384603]\) | \(2141202151369/5832225\) | \(101575630408251168225\) | \([2, 2]\) | \(17842176\) | \(2.7125\) | |
| 388815.cy3 | 388815cy4 | \([1, 1, 0, -4238623, 12621892102]\) | \(-483551781049/3672913125\) | \(-63968462483291509513125\) | \([2]\) | \(35684352\) | \(3.0590\) | |
| 388815.cy4 | 388815cy1 | \([1, 1, 0, -609683, 13140072]\) | \(1439069689/828345\) | \(14426683739142919545\) | \([2]\) | \(8921088\) | \(2.3659\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 388815.cy have rank \(1\).
Complex multiplication
The elliptic curves in class 388815.cy do not have complex multiplication.Modular form 388815.2.a.cy
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 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.
