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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 27797.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 27797.d1 | 27797d1 | \([0, -1, 1, -32249, -2218362]\) | \(-78843215872/539\) | \(-25357729859\) | \([]\) | \(47520\) | \(1.1772\) | \(\Gamma_0(N)\)-optimal |
| 27797.d2 | 27797d2 | \([0, -1, 1, -17809, -4223717]\) | \(-13278380032/156590819\) | \(-7366953036366539\) | \([]\) | \(142560\) | \(1.7265\) | |
| 27797.d3 | 27797d3 | \([0, -1, 1, 159081, 109428108]\) | \(9463555063808/115539436859\) | \(-5435654597275527779\) | \([]\) | \(427680\) | \(2.2758\) |
Rank
sage: E.rank()
The elliptic curves in class 27797.d have rank \(1\).
Complex multiplication
The elliptic curves in class 27797.d do not have complex multiplication.Modular form 27797.2.a.d
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
