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SageMath
E = EllipticCurve("dl1")
E.isogeny_class()
Elliptic curves in class 39600dl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 39600.f4 | 39600dl1 | \([0, 0, 0, -10200, 388375]\) | \(643956736/15125\) | \(2756531250000\) | \([2]\) | \(82944\) | \(1.1726\) | \(\Gamma_0(N)\)-optimal |
| 39600.f3 | 39600dl2 | \([0, 0, 0, -22575, -737750]\) | \(436334416/171875\) | \(501187500000000\) | \([2]\) | \(165888\) | \(1.5192\) | |
| 39600.f2 | 39600dl3 | \([0, 0, 0, -100200, -12054125]\) | \(610462990336/8857805\) | \(1614334961250000\) | \([2]\) | \(248832\) | \(1.7219\) | |
| 39600.f1 | 39600dl4 | \([0, 0, 0, -1597575, -777212750]\) | \(154639330142416/33275\) | \(97029900000000\) | \([2]\) | \(497664\) | \(2.0685\) |
Rank
sage: E.rank()
The elliptic curves in class 39600dl have rank \(1\).
Complex multiplication
The elliptic curves in class 39600dl do not have complex multiplication.Modular form 39600.2.a.dl
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
