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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 25152b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 25152.j2 | 25152b1 | \([0, -1, 0, -136641, 18524097]\) | \(1076291879750641/60150618144\) | \(15768123642740736\) | \([]\) | \(161280\) | \(1.8631\) | \(\Gamma_0(N)\)-optimal |
| 25152.j1 | 25152b2 | \([0, -1, 0, -14530881, -21315070143]\) | \(1294373635812597347281/2083292441154\) | \(546122613693874176\) | \([]\) | \(806400\) | \(2.6678\) |
Rank
sage: E.rank()
The elliptic curves in class 25152b have rank \(1\).
Complex multiplication
The elliptic curves in class 25152b do not have complex multiplication.Modular form 25152.2.a.b
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
