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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 274890d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
274890.d2 | 274890d1 | \([1, 1, 0, -5023, 19100677]\) | \(-347428927/3906355200\) | \(-157635522543206400\) | \([2]\) | \(3813376\) | \(1.9788\) | \(\Gamma_0(N)\)-optimal |
274890.d1 | 274890d2 | \([1, 1, 0, -1102623, 439042437]\) | \(3673864287576127/58210796160\) | \(2349015591397749120\) | \([2]\) | \(7626752\) | \(2.3254\) |
Rank
sage: E.rank()
The elliptic curves in class 274890d have rank \(1\).
Complex multiplication
The elliptic curves in class 274890d do not have complex multiplication.Modular form 274890.2.a.d
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.