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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 303646t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
303646.t2 | 303646t1 | \([1, -1, 1, -10237572, -11603238873]\) | \(801581275315909089/70810888830976\) | \(10482552878973702897664\) | \([]\) | \(43464960\) | \(2.9655\) | \(\Gamma_0(N)\)-optimal |
303646.t1 | 303646t2 | \([1, -1, 1, -5084384412, 139543508251047]\) | \(98191033604529537629349729/10906239337336\) | \(1614514835949305651704\) | \([]\) | \(304254720\) | \(3.9385\) |
Rank
sage: E.rank()
The elliptic curves in class 303646t have rank \(1\).
Complex multiplication
The elliptic curves in class 303646t do not have complex multiplication.Modular form 303646.2.a.t
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.