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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 33600.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 33600.l1 | 33600m6 | \([0, -1, 0, -2440033, -1465868063]\) | \(784478485879202/221484375\) | \(453600000000000000\) | \([2]\) | \(786432\) | \(2.3690\) | |
| 33600.l2 | 33600m4 | \([0, -1, 0, -172033, -16616063]\) | \(549871953124/200930625\) | \(205752960000000000\) | \([2, 2]\) | \(393216\) | \(2.0225\) | |
| 33600.l3 | 33600m2 | \([0, -1, 0, -74033, 7589937]\) | \(175293437776/4862025\) | \(1244678400000000\) | \([2, 2]\) | \(196608\) | \(1.6759\) | |
| 33600.l4 | 33600m1 | \([0, -1, 0, -73533, 7699437]\) | \(2748251600896/2205\) | \(35280000000\) | \([2]\) | \(98304\) | \(1.3293\) | \(\Gamma_0(N)\)-optimal |
| 33600.l5 | 33600m3 | \([0, -1, 0, 15967, 24779937]\) | \(439608956/259416045\) | \(-265642030080000000\) | \([2]\) | \(393216\) | \(2.0225\) | |
| 33600.l6 | 33600m5 | \([0, -1, 0, 527967, -118116063]\) | \(7947184069438/7533176175\) | \(-15427944806400000000\) | \([2]\) | \(786432\) | \(2.3690\) |
Rank
sage: E.rank()
The elliptic curves in class 33600.l have rank \(1\).
Complex multiplication
The elliptic curves in class 33600.l do not have complex multiplication.Modular form 33600.2.a.l
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 8 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
