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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 14350b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14350.i2 | 14350b1 | \([1, -1, 0, -483817, 119355341]\) | \(801581275315909089/70810888830976\) | \(1106420137984000000\) | \([]\) | \(493920\) | \(2.2025\) | \(\Gamma_0(N)\)-optimal |
14350.i1 | 14350b2 | \([1, -1, 0, -240282817, -1433553773659]\) | \(98191033604529537629349729/10906239337336\) | \(170409989645875000\) | \([]\) | \(3457440\) | \(3.1755\) |
Rank
sage: E.rank()
The elliptic curves in class 14350b have rank \(1\).
Complex multiplication
The elliptic curves in class 14350b do not have complex multiplication.Modular form 14350.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.