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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 57420.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 57420.q1 | 57420m1 | \([0, 0, 0, -7884012, -8520577391]\) | \(4646415367355940880384/38478378125\) | \(448811802450000\) | \([2]\) | \(1128960\) | \(2.3993\) | \(\Gamma_0(N)\)-optimal |
| 57420.q2 | 57420m2 | \([0, 0, 0, -7878567, -8532934274]\) | \(-289799689905740628304/835751962890625\) | \(-155971374322500000000\) | \([2]\) | \(2257920\) | \(2.7458\) |
Rank
sage: E.rank()
The elliptic curves in class 57420.q have rank \(0\).
Complex multiplication
The elliptic curves in class 57420.q do not have complex multiplication.Modular form 57420.2.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 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.
