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SageMath
E = EllipticCurve("di1")
E.isogeny_class()
Elliptic curves in class 68400di
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 68400.bo2 | 68400di1 | \([0, 0, 0, 290925, 41735250]\) | \(2161700757/1848320\) | \(-2328350883840000000\) | \([2]\) | \(1105920\) | \(2.2119\) | \(\Gamma_0(N)\)-optimal |
| 68400.bo1 | 68400di2 | \([0, 0, 0, -1437075, 368327250]\) | \(260549802603/104256800\) | \(131333542041600000000\) | \([2]\) | \(2211840\) | \(2.5585\) |
Rank
sage: E.rank()
The elliptic curves in class 68400di have rank \(0\).
Complex multiplication
The elliptic curves in class 68400di do not have complex multiplication.Modular form 68400.2.a.di
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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
