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SageMath
sage: E = EllipticCurve("b1")
sage: E.isogeny_class()
Elliptic curves in class 7220.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7220.b1 | 7220d1 | \([0, 1, 0, -332601, -68967860]\) | \(5405726654464/407253125\) | \(306553312890050000\) | \([2]\) | \(86400\) | \(2.1006\) | \(\Gamma_0(N)\)-optimal |
| 7220.b2 | 7220d2 | \([0, 1, 0, 319004, -305630796]\) | \(298091207216/3525390625\) | \(-42458907602500000000\) | \([2]\) | \(172800\) | \(2.4472\) |
Rank
sage: E.rank()
The elliptic curves in class 7220.b have rank \(1\).
Complex multiplication
The elliptic curves in class 7220.b do not have complex multiplication.Modular form 7220.2.a.b
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.
