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SageMath
E = EllipticCurve("eq1")
E.isogeny_class()
Elliptic curves in class 88200eq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 88200.cw2 | 88200eq1 | \([0, 0, 0, -7350, -385875]\) | \(-55296/49\) | \(-38912406750000\) | \([2]\) | \(196608\) | \(1.3048\) | \(\Gamma_0(N)\)-optimal |
| 88200.cw1 | 88200eq2 | \([0, 0, 0, -135975, -19293750]\) | \(21882096/7\) | \(88942644000000\) | \([2]\) | \(393216\) | \(1.6514\) |
Rank
sage: E.rank()
The elliptic curves in class 88200eq have rank \(1\).
Complex multiplication
The elliptic curves in class 88200eq do not have complex multiplication.Modular form 88200.2.a.eq
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.
