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SageMath
E = EllipticCurve("di1")
E.isogeny_class()
Elliptic curves in class 19600di
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 19600.dn2 | 19600di1 | \([0, -1, 0, -157208, -20067088]\) | \(46585/8\) | \(73789452800000000\) | \([]\) | \(181440\) | \(1.9570\) | \(\Gamma_0(N)\)-optimal |
| 19600.dn1 | 19600di2 | \([0, -1, 0, -3587208, 2614172912]\) | \(553463785/512\) | \(4722524979200000000\) | \([]\) | \(544320\) | \(2.5063\) |
Rank
sage: E.rank()
The elliptic curves in class 19600di have rank \(1\).
Complex multiplication
The elliptic curves in class 19600di do not have complex multiplication.Modular form 19600.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
