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SageMath
E = EllipticCurve("mn1")
E.isogeny_class()
Elliptic curves in class 381150.mn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 381150.mn1 | 381150mn1 | \([1, -1, 1, -139506005, 632880813997]\) | \(551105805571803/1376829440\) | \(750149066476212480000000\) | \([2]\) | \(103219200\) | \(3.4586\) | \(\Gamma_0(N)\)-optimal |
| 381150.mn2 | 381150mn2 | \([1, -1, 1, -87234005, 1112842317997]\) | \(-134745327251163/903920796800\) | \(-492490443760379029350000000\) | \([2]\) | \(206438400\) | \(3.8052\) |
Rank
sage: E.rank()
The elliptic curves in class 381150.mn have rank \(1\).
Complex multiplication
The elliptic curves in class 381150.mn do not have complex multiplication.Modular form 381150.2.a.mn
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.
