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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 15730y
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 15730.s2 | 15730y1 | \([1, 0, 0, -3935, -94775]\) | \(3803721481/26000\) | \(46060586000\) | \([2]\) | \(25920\) | \(0.88009\) | \(\Gamma_0(N)\)-optimal |
| 15730.s3 | 15730y2 | \([1, 0, 0, -1515, -209483]\) | \(-217081801/10562500\) | \(-18712113062500\) | \([2]\) | \(51840\) | \(1.2267\) | |
| 15730.s1 | 15730y3 | \([1, 0, 0, -25110, 1467940]\) | \(988345570681/44994560\) | \(79710607708160\) | \([2]\) | \(77760\) | \(1.4294\) | |
| 15730.s4 | 15730y4 | \([1, 0, 0, 13610, 5595492]\) | \(157376536199/7722894400\) | \(-13681578526158400\) | \([2]\) | \(155520\) | \(1.7760\) |
Rank
sage: E.rank()
The elliptic curves in class 15730y have rank \(0\).
Complex multiplication
The elliptic curves in class 15730y do not have complex multiplication.Modular form 15730.2.a.y
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
