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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 225264.i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 225264.i1 | 225264ck4 | \([0, -1, 0, -109864, -13636160]\) | \(3044193988/85293\) | \(4108988752008192\) | \([2]\) | \(1548288\) | \(1.7751\) | |
| 225264.i2 | 225264ck2 | \([0, -1, 0, -16004, 480384]\) | \(37642192/13689\) | \(164866832642304\) | \([2, 2]\) | \(774144\) | \(1.4285\) | |
| 225264.i3 | 225264ck1 | \([0, -1, 0, -14199, 655830]\) | \(420616192/117\) | \(88069889232\) | \([2]\) | \(387072\) | \(1.0819\) | \(\Gamma_0(N)\)-optimal |
| 225264.i4 | 225264ck3 | \([0, -1, 0, 48976, 3339504]\) | \(269676572/257049\) | \(-12383330985133056\) | \([2]\) | \(1548288\) | \(1.7751\) |
Rank
sage: E.rank()
The elliptic curves in class 225264.i have rank \(0\).
Complex multiplication
The elliptic curves in class 225264.i do not have complex multiplication.Modular form 225264.2.a.i
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.
