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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 3330.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3330.m1 | 3330s4 | \([1, -1, 1, -94388, 5005847]\) | \(127568139540190201/59114336463360\) | \(43094351281789440\) | \([6]\) | \(48384\) | \(1.8864\) | |
| 3330.m2 | 3330s2 | \([1, -1, 1, -47813, -4011883]\) | \(16581570075765001/998001000\) | \(727542729000\) | \([2]\) | \(16128\) | \(1.3371\) | |
| 3330.m3 | 3330s1 | \([1, -1, 1, -2813, -69883]\) | \(-3375675045001/999000000\) | \(-728271000000\) | \([2]\) | \(8064\) | \(0.99057\) | \(\Gamma_0(N)\)-optimal |
| 3330.m4 | 3330s3 | \([1, -1, 1, 20812, 582167]\) | \(1367594037332999/995878502400\) | \(-725995428249600\) | \([6]\) | \(24192\) | \(1.5399\) |
Rank
sage: E.rank()
The elliptic curves in class 3330.m have rank \(0\).
Complex multiplication
The elliptic curves in class 3330.m do not have complex multiplication.Modular form 3330.2.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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
