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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 4560l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4560.c4 | 4560l1 | \([0, -1, 0, -1221, -16020]\) | \(12592337649664/1315845\) | \(21053520\) | \([2]\) | \(2304\) | \(0.43718\) | \(\Gamma_0(N)\)-optimal |
4560.c3 | 4560l2 | \([0, -1, 0, -1316, -13284]\) | \(985329269584/252434475\) | \(64623225600\) | \([2]\) | \(4608\) | \(0.78375\) | |
4560.c2 | 4560l3 | \([0, -1, 0, -2661, 29736]\) | \(130287139815424/52926616125\) | \(846825858000\) | \([2]\) | \(6912\) | \(0.98648\) | |
4560.c1 | 4560l4 | \([0, -1, 0, -36956, 2745900]\) | \(21804712949838544/8680921875\) | \(2222316000000\) | \([2]\) | \(13824\) | \(1.3331\) |
Rank
sage: E.rank()
The elliptic curves in class 4560l have rank \(0\).
Complex multiplication
The elliptic curves in class 4560l do not have complex multiplication.Modular form 4560.2.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 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.