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SageMath
E = EllipticCurve("dn1")
E.isogeny_class()
Elliptic curves in class 25200.dn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 25200.dn1 | 25200eq3 | \([0, 0, 0, -472800, -130898000]\) | \(-250523582464/13671875\) | \(-637875000000000000\) | \([]\) | \(311040\) | \(2.1746\) | |
| 25200.dn2 | 25200eq1 | \([0, 0, 0, -4800, 142000]\) | \(-262144/35\) | \(-1632960000000\) | \([]\) | \(34560\) | \(1.0760\) | \(\Gamma_0(N)\)-optimal |
| 25200.dn3 | 25200eq2 | \([0, 0, 0, 31200, -362000]\) | \(71991296/42875\) | \(-2000376000000000\) | \([]\) | \(103680\) | \(1.6253\) |
Rank
sage: E.rank()
The elliptic curves in class 25200.dn have rank \(0\).
Complex multiplication
The elliptic curves in class 25200.dn do not have complex multiplication.Modular form 25200.2.a.dn
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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
