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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 87360a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 87360.l3 | 87360a1 | \([0, -1, 0, -476, 3990]\) | \(186756901696/8996715\) | \(575789760\) | \([2]\) | \(40960\) | \(0.44095\) | \(\Gamma_0(N)\)-optimal |
| 87360.l2 | 87360a2 | \([0, -1, 0, -1321, -13079]\) | \(62287505344/16769025\) | \(68685926400\) | \([2, 2]\) | \(81920\) | \(0.78753\) | |
| 87360.l4 | 87360a3 | \([0, -1, 0, 3359, -88895]\) | \(127871714872/175573125\) | \(-5753180160000\) | \([2]\) | \(163840\) | \(1.1341\) | |
| 87360.l1 | 87360a4 | \([0, -1, 0, -19521, -1043199]\) | \(25107427013768/2985255\) | \(97820835840\) | \([2]\) | \(163840\) | \(1.1341\) |
Rank
sage: E.rank()
The elliptic curves in class 87360a have rank \(1\).
Complex multiplication
The elliptic curves in class 87360a do not have complex multiplication.Modular form 87360.2.a.a
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
