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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 13860.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 13860.h1 | 13860m2 | \([0, 0, 0, -37623, -2599522]\) | \(31558509702736/2620631475\) | \(489072728390400\) | \([2]\) | \(55296\) | \(1.5608\) | |
| 13860.h2 | 13860m1 | \([0, 0, 0, 2472, -185803]\) | \(143225913344/1361505915\) | \(-15880604992560\) | \([2]\) | \(27648\) | \(1.2142\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 13860.h have rank \(0\).
Complex multiplication
The elliptic curves in class 13860.h do not have complex multiplication.Modular form 13860.2.a.h
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.
