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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 302330r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 302330.r2 | 302330r1 | \([1, 1, 0, -1082, 184724]\) | \(-2863099371769/300652944640\) | \(-14731994287360\) | \([]\) | \(1123200\) | \(1.2063\) | \(\Gamma_0(N)\)-optimal |
| 302330.r1 | 302330r2 | \([1, 1, 0, -281817, 57467621]\) | \(-50516307977225837929/1293942784000\) | \(-63403196416000\) | \([]\) | \(3369600\) | \(1.7556\) |
Rank
sage: E.rank()
The elliptic curves in class 302330r have rank \(0\).
Complex multiplication
The elliptic curves in class 302330r do not have complex multiplication.Modular form 302330.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
