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SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 121296.bm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 121296.bm1 | 121296f4 | \([0, -1, 0, -1455672, 676480320]\) | \(7080974546692/189\) | \(9105071625216\) | \([2]\) | \(1327104\) | \(2.0004\) | |
| 121296.bm2 | 121296f3 | \([0, -1, 0, -141632, -2413392]\) | \(6522128932/3720087\) | \(179215124799126528\) | \([2]\) | \(1327104\) | \(2.0004\) | |
| 121296.bm3 | 121296f2 | \([0, -1, 0, -91092, 10565280]\) | \(6940769488/35721\) | \(430214634291456\) | \([2, 2]\) | \(663552\) | \(1.6538\) | |
| 121296.bm4 | 121296f1 | \([0, -1, 0, -2647, 341038]\) | \(-2725888/64827\) | \(-48797493241392\) | \([2]\) | \(331776\) | \(1.3073\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 121296.bm have rank \(0\).
Complex multiplication
The elliptic curves in class 121296.bm do not have complex multiplication.Modular form 121296.2.a.bm
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.
