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SageMath
E = EllipticCurve("dy1")
E.isogeny_class()
Elliptic curves in class 40768dy
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 40768.dl2 | 40768dy1 | \([0, -1, 0, -1437, 21491]\) | \(-43614208/91\) | \(-685187776\) | \([]\) | \(27648\) | \(0.58102\) | \(\Gamma_0(N)\)-optimal |
| 40768.dl3 | 40768dy2 | \([0, -1, 0, 2483, 103419]\) | \(224755712/753571\) | \(-5674039973056\) | \([]\) | \(82944\) | \(1.1303\) | |
| 40768.dl1 | 40768dy3 | \([0, -1, 0, -22997, -3300709]\) | \(-178643795968/524596891\) | \(-3949971176272576\) | \([]\) | \(248832\) | \(1.6796\) |
Rank
sage: E.rank()
The elliptic curves in class 40768dy have rank \(0\).
Complex multiplication
The elliptic curves in class 40768dy do not have complex multiplication.Modular form 40768.2.a.dy
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
