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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 346560.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 346560.d1 | 346560d4 | \([0, -1, 0, -1328961, -558881535]\) | \(168379496648/9774075\) | \(15067708435171737600\) | \([2]\) | \(8847360\) | \(2.4337\) | |
| 346560.d2 | 346560d2 | \([0, -1, 0, -245961, 36118665]\) | \(8539701184/2030625\) | \(391301292464640000\) | \([2, 2]\) | \(4423680\) | \(2.0871\) | |
| 346560.d3 | 346560d1 | \([0, -1, 0, -229716, 42450966]\) | \(445243675456/38475\) | \(115845777374400\) | \([2]\) | \(2211840\) | \(1.7405\) | \(\Gamma_0(N)\)-optimal |
| 346560.d4 | 346560d3 | \([0, -1, 0, 577119, 225591681]\) | \(13789468792/22265625\) | \(-34324674777600000000\) | \([2]\) | \(8847360\) | \(2.4337\) |
Rank
sage: E.rank()
The elliptic curves in class 346560.d have rank \(0\).
Complex multiplication
The elliptic curves in class 346560.d do not have complex multiplication.Modular form 346560.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
