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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 87360e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 87360.c3 | 87360e1 | \([0, -1, 0, -9121, -332255]\) | \(320153881321/6825\) | \(1789132800\) | \([2]\) | \(98304\) | \(0.89270\) | \(\Gamma_0(N)\)-optimal |
| 87360.c2 | 87360e2 | \([0, -1, 0, -9441, -307359]\) | \(355045312441/46580625\) | \(12210831360000\) | \([2, 2]\) | \(196608\) | \(1.2393\) | |
| 87360.c4 | 87360e3 | \([0, -1, 0, 14559, -1636959]\) | \(1301812981559/5143122075\) | \(-1348238593228800\) | \([2]\) | \(393216\) | \(1.5858\) | |
| 87360.c1 | 87360e4 | \([0, -1, 0, -38561, 2610465]\) | \(24190225473961/2879296875\) | \(754790400000000\) | \([2]\) | \(393216\) | \(1.5858\) |
Rank
sage: E.rank()
The elliptic curves in class 87360e have rank \(1\).
Complex multiplication
The elliptic curves in class 87360e do not have complex multiplication.Modular form 87360.2.a.e
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.
