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SageMath
E = EllipticCurve("dv1")
E.isogeny_class()
Elliptic curves in class 39600dv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 39600.ea4 | 39600dv1 | \([0, 0, 0, 49200, -15433625]\) | \(72268906496/606436875\) | \(-110523120468750000\) | \([2]\) | \(221184\) | \(1.9517\) | \(\Gamma_0(N)\)-optimal |
| 39600.ea3 | 39600dv2 | \([0, 0, 0, -710175, -212111750]\) | \(13584145739344/1195803675\) | \(3486963516300000000\) | \([2]\) | \(442368\) | \(2.2983\) | |
| 39600.ea2 | 39600dv3 | \([0, 0, 0, -3514800, -2538300125]\) | \(-26348629355659264/24169921875\) | \(-4404968261718750000\) | \([2]\) | \(663552\) | \(2.5010\) | |
| 39600.ea1 | 39600dv4 | \([0, 0, 0, -56249175, -162376190750]\) | \(6749703004355978704/5671875\) | \(16539187500000000\) | \([2]\) | \(1327104\) | \(2.8476\) |
Rank
sage: E.rank()
The elliptic curves in class 39600dv have rank \(0\).
Complex multiplication
The elliptic curves in class 39600dv do not have complex multiplication.Modular form 39600.2.a.dv
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.
