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SageMath
E = EllipticCurve("dk1")
E.isogeny_class()
Elliptic curves in class 72450.dk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 72450.dk1 | 72450cn1 | \([1, -1, 1, -347930, 123794697]\) | \(-17665842966075/14850127376\) | \(-3915560929218750000\) | \([]\) | \(1347840\) | \(2.2654\) | \(\Gamma_0(N)\)-optimal |
| 72450.dk2 | 72450cn2 | \([1, -1, 1, 2867695, -2028530303]\) | \(13568486147325/17093758976\) | \(-3285707596920000000000\) | \([]\) | \(4043520\) | \(2.8147\) |
Rank
sage: E.rank()
The elliptic curves in class 72450.dk have rank \(1\).
Complex multiplication
The elliptic curves in class 72450.dk do not have complex multiplication.Modular form 72450.2.a.dk
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
