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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 337896r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 337896.r1 | 337896r1 | \([0, 0, 0, -10830, -198911]\) | \(256000/117\) | \(64202949250128\) | \([2]\) | \(884736\) | \(1.3444\) | \(\Gamma_0(N)\)-optimal |
| 337896.r2 | 337896r2 | \([0, 0, 0, 37905, -1495262]\) | \(686000/507\) | \(-4451404481342208\) | \([2]\) | \(1769472\) | \(1.6909\) |
Rank
sage: E.rank()
The elliptic curves in class 337896r have rank \(0\).
Complex multiplication
The elliptic curves in class 337896r do not have complex multiplication.Modular form 337896.2.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.
