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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 382200.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 382200.m1 | 382200m1 | \([0, -1, 0, -3267158708, -71877969906588]\) | \(65565618540844760336/188428167837\) | \(11084192758927606500000000\) | \([2]\) | \(225607680\) | \(4.0362\) | \(\Gamma_0(N)\)-optimal |
| 382200.m2 | 382200m2 | \([0, -1, 0, -3225141208, -73816741391588]\) | \(-15767094823546327124/879851321206767\) | \(-207027256177309861566000000000\) | \([2]\) | \(451215360\) | \(4.3827\) |
Rank
sage: E.rank()
The elliptic curves in class 382200.m have rank \(0\).
Complex multiplication
The elliptic curves in class 382200.m do not have complex multiplication.Modular form 382200.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
