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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 154560.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 154560.m1 | 154560hz4 | \([0, -1, 0, -81121, -8854079]\) | \(1801685643226568/2795664375\) | \(91608330240000\) | \([2]\) | \(655360\) | \(1.5780\) | |
| 154560.m2 | 154560hz2 | \([0, -1, 0, -6601, -45815]\) | \(7767097430464/4251692025\) | \(17414930534400\) | \([2, 2]\) | \(327680\) | \(1.2314\) | |
| 154560.m3 | 154560hz1 | \([0, -1, 0, -3956, 96486]\) | \(107009507066176/793349235\) | \(50774351040\) | \([2]\) | \(163840\) | \(0.88485\) | \(\Gamma_0(N)\)-optimal |
| 154560.m4 | 154560hz3 | \([0, -1, 0, 25599, -387135]\) | \(56614257100792/34652610405\) | \(-1135496737751040\) | \([2]\) | \(655360\) | \(1.5780\) |
Rank
sage: E.rank()
The elliptic curves in class 154560.m have rank \(0\).
Complex multiplication
The elliptic curves in class 154560.m do not have complex multiplication.Modular form 154560.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
