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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 6672.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6672.f1 | 6672g2 | \([0, -1, 0, -732, -7380]\) | \(169671989968/101331\) | \(25940736\) | \([2]\) | \(3024\) | \(0.36669\) | |
| 6672.f2 | 6672g1 | \([0, -1, 0, -37, -152]\) | \(-359661568/521667\) | \(-8346672\) | \([2]\) | \(1512\) | \(0.020115\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6672.f have rank \(0\).
Complex multiplication
The elliptic curves in class 6672.f do not have complex multiplication.Modular form 6672.2.a.f
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 LMFDB 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 LMFDB labels.
