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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 101430.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 101430.m1 | 101430bm4 | \([1, -1, 0, -609643260, -5793624635184]\) | \(292169767125103365085489/72534787200\) | \(6221027335704451200\) | \([2]\) | \(22020096\) | \(3.4219\) | |
| 101430.m2 | 101430bm3 | \([1, -1, 0, -44598780, -57556234800]\) | \(114387056741228939569/49503729150000000\) | \(4245742824230127150000000\) | \([2]\) | \(22020096\) | \(3.4219\) | |
| 101430.m3 | 101430bm2 | \([1, -1, 0, -38107260, -90495505584]\) | \(71356102305927901489/35540674560000\) | \(3048185794734581760000\) | \([2, 2]\) | \(11010048\) | \(3.0753\) | |
| 101430.m4 | 101430bm1 | \([1, -1, 0, -1980540, -1905562800]\) | \(-10017490085065009/12502381363200\) | \(-1072280752784356147200\) | \([2]\) | \(5505024\) | \(2.7287\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 101430.m have rank \(0\).
Complex multiplication
The elliptic curves in class 101430.m do not have complex multiplication.Modular form 101430.2.a.m
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.
