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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 203840q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 203840.m1 | 203840q1 | \([0, 1, 0, -2637441, -1649280641]\) | \(65787589563409/10400000\) | \(320746186342400000\) | \([2]\) | \(4423680\) | \(2.3696\) | \(\Gamma_0(N)\)-optimal |
| 203840.m2 | 203840q2 | \([0, 1, 0, -2386561, -1975374465]\) | \(-48743122863889/26406250000\) | \(-814394613760000000000\) | \([2]\) | \(8847360\) | \(2.7162\) |
Rank
sage: E.rank()
The elliptic curves in class 203840q have rank \(1\).
Complex multiplication
The elliptic curves in class 203840q do not have complex multiplication.Modular form 203840.2.a.q
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.
