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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 38829.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 38829.d1 | 38829b3 | \([0, -1, 1, -14200344653, 651327773598287]\) | \(-50096759460260217094144000/18963\) | \(-119872007498187\) | \([]\) | \(15168384\) | \(3.9438\) | |
| 38829.d2 | 38829b2 | \([0, -1, 1, -175309853, 893538253106]\) | \(-94260981564964864000/6819006982347\) | \(-43105418769081321096003\) | \([]\) | \(5056128\) | \(3.3945\) | |
| 38829.d3 | 38829b1 | \([0, -1, 1, -80123, 3456143729]\) | \(-8998912000/816294970323\) | \(-5160096862484363794827\) | \([]\) | \(1685376\) | \(2.8452\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 38829.d have rank \(0\).
Complex multiplication
The elliptic curves in class 38829.d do not have complex multiplication.Modular form 38829.2.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.
