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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 103056u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 103056.o1 | 103056u1 | \([0, -1, 0, -6972872, 7089373680]\) | \(9153747013124116391113/5485837418496\) | \(22469990066159616\) | \([2]\) | \(2612736\) | \(2.4604\) | \(\Gamma_0(N)\)-optimal |
| 103056.o2 | 103056u2 | \([0, -1, 0, -6931912, 7176733168]\) | \(-8993380100968273380553/224220843480310272\) | \(-918408574895350874112\) | \([2]\) | \(5225472\) | \(2.8070\) |
Rank
sage: E.rank()
The elliptic curves in class 103056u have rank \(0\).
Complex multiplication
The elliptic curves in class 103056u do not have complex multiplication.Modular form 103056.2.a.u
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
