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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 1170.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1170.m1 | 1170m3 | \([1, -1, 1, -4352, 111561]\) | \(12501706118329/2570490\) | \(1873887210\) | \([2]\) | \(1024\) | \(0.77634\) | |
| 1170.m2 | 1170m2 | \([1, -1, 1, -302, 1401]\) | \(4165509529/1368900\) | \(997928100\) | \([2, 2]\) | \(512\) | \(0.42977\) | |
| 1170.m3 | 1170m1 | \([1, -1, 1, -122, -471]\) | \(273359449/9360\) | \(6823440\) | \([2]\) | \(256\) | \(0.083192\) | \(\Gamma_0(N)\)-optimal |
| 1170.m4 | 1170m4 | \([1, -1, 1, 868, 8889]\) | \(99317171591/106616250\) | \(-77723246250\) | \([2]\) | \(1024\) | \(0.77634\) |
Rank
sage: E.rank()
The elliptic curves in class 1170.m have rank \(0\).
Complex multiplication
The elliptic curves in class 1170.m do not have complex multiplication.Modular form 1170.2.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.
