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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 3168.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3168.a1 | 3168i3 | \([0, 0, 0, -2822691, 1825337270]\) | \(6663712298552914184/29403\) | \(10974610944\) | \([4]\) | \(30720\) | \(2.0131\) | |
| 3168.a2 | 3168i2 | \([0, 0, 0, -187356, 24784544]\) | \(243578556889408/52089208083\) | \(155537541908508672\) | \([2]\) | \(30720\) | \(2.0131\) | |
| 3168.a3 | 3168i1 | \([0, 0, 0, -176421, 28519940]\) | \(13015685560572352/864536409\) | \(40335810698304\) | \([2, 2]\) | \(15360\) | \(1.6665\) | \(\Gamma_0(N)\)-optimal |
| 3168.a4 | 3168i4 | \([0, 0, 0, -165531, 32194226]\) | \(-1343891598641864/421900912521\) | \(-157473671796638208\) | \([2]\) | \(30720\) | \(2.0131\) |
Rank
sage: E.rank()
The elliptic curves in class 3168.a have rank \(0\).
Complex multiplication
The elliptic curves in class 3168.a do not have complex multiplication.Modular form 3168.2.a.a
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
