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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 18032.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
18032.l1 | 18032x3 | \([0, 0, 0, -96971, 11620154]\) | \(209267191953/55223\) | \(26611428257792\) | \([2]\) | \(61440\) | \(1.5605\) | |
18032.l2 | 18032x2 | \([0, 0, 0, -6811, 133770]\) | \(72511713/25921\) | \(12491078569984\) | \([2, 2]\) | \(30720\) | \(1.2139\) | |
18032.l3 | 18032x1 | \([0, 0, 0, -2891, -58310]\) | \(5545233/161\) | \(77584338944\) | \([2]\) | \(15360\) | \(0.86732\) | \(\Gamma_0(N)\)-optimal |
18032.l4 | 18032x4 | \([0, 0, 0, 20629, 940506]\) | \(2014698447/1958887\) | \(-943968651931648\) | \([4]\) | \(61440\) | \(1.5605\) |
Rank
sage: E.rank()
The elliptic curves in class 18032.l have rank \(2\).
Complex multiplication
The elliptic curves in class 18032.l do not have complex multiplication.Modular form 18032.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.