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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 349140r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
349140.r2 | 349140r1 | \([0, -1, 0, -705, -116478]\) | \(-16384/2475\) | \(-5862221204400\) | \([2]\) | \(540672\) | \(1.1293\) | \(\Gamma_0(N)\)-optimal |
349140.r1 | 349140r2 | \([0, -1, 0, -40380, -3084168]\) | \(192143824/1815\) | \(68783395464960\) | \([2]\) | \(1081344\) | \(1.4759\) |
Rank
sage: E.rank()
The elliptic curves in class 349140r have rank \(2\).
Complex multiplication
The elliptic curves in class 349140r do not have complex multiplication.Modular form 349140.2.a.r
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.