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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 25152h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 25152.u2 | 25152h1 | \([0, -1, 0, -2529, 49761]\) | \(6826561273/7074\) | \(1854406656\) | \([]\) | \(29184\) | \(0.69615\) | \(\Gamma_0(N)\)-optimal |
| 25152.u1 | 25152h2 | \([0, -1, 0, -9249, -287583]\) | \(333822098953/53954184\) | \(14143765610496\) | \([]\) | \(87552\) | \(1.2455\) |
Rank
sage: E.rank()
The elliptic curves in class 25152h have rank \(0\).
Complex multiplication
The elliptic curves in class 25152h do not have complex multiplication.Modular form 25152.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
