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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 112632y
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 112632.s3 | 112632y1 | \([0, 1, 0, -14199, -655830]\) | \(420616192/117\) | \(88069889232\) | \([2]\) | \(193536\) | \(1.0819\) | \(\Gamma_0(N)\)-optimal |
| 112632.s2 | 112632y2 | \([0, 1, 0, -16004, -480384]\) | \(37642192/13689\) | \(164866832642304\) | \([2, 2]\) | \(387072\) | \(1.4285\) | |
| 112632.s4 | 112632y3 | \([0, 1, 0, 48976, -3339504]\) | \(269676572/257049\) | \(-12383330985133056\) | \([2]\) | \(774144\) | \(1.7751\) | |
| 112632.s1 | 112632y4 | \([0, 1, 0, -109864, 13636160]\) | \(3044193988/85293\) | \(4108988752008192\) | \([2]\) | \(774144\) | \(1.7751\) |
Rank
sage: E.rank()
The elliptic curves in class 112632y have rank \(0\).
Complex multiplication
The elliptic curves in class 112632y do not have complex multiplication.Modular form 112632.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
