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SageMath
E = EllipticCurve("fb1")
E.isogeny_class()
Elliptic curves in class 91200.fb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 91200.fb1 | 91200ea4 | \([0, 1, 0, -1973509633, -33745354847137]\) | \(207530301091125281552569/805586668007040\) | \(3299682992156835840000000\) | \([2]\) | \(41287680\) | \(3.9178\) | |
| 91200.fb2 | 91200ea3 | \([0, 1, 0, -374021633, 2149549984863]\) | \(1412712966892699019449/330160465517040000\) | \(1352337266757795840000000000\) | \([2]\) | \(41287680\) | \(3.9178\) | |
| 91200.fb3 | 91200ea2 | \([0, 1, 0, -125189633, -510712927137]\) | \(52974743974734147769/3152005008998400\) | \(12910612516857446400000000\) | \([2, 2]\) | \(20643840\) | \(3.5713\) | |
| 91200.fb4 | 91200ea1 | \([0, 1, 0, 5882367, -32955487137]\) | \(5495662324535111/117739817533440\) | \(-482262292616970240000000\) | \([2]\) | \(10321920\) | \(3.2247\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 91200.fb have rank \(1\).
Complex multiplication
The elliptic curves in class 91200.fb do not have complex multiplication.Modular form 91200.2.a.fb
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
