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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 8512.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 8512.b1 | 8512c1 | \([0, 0, 0, -451, -3684]\) | \(158516094528/123823\) | \(7924672\) | \([2]\) | \(1728\) | \(0.25495\) | \(\Gamma_0(N)\)-optimal |
| 8512.b2 | 8512c2 | \([0, 0, 0, -356, -5280]\) | \(-1218186432/2235331\) | \(-9155915776\) | \([2]\) | \(3456\) | \(0.60152\) |
Rank
sage: E.rank()
The elliptic curves in class 8512.b have rank \(0\).
Complex multiplication
The elliptic curves in class 8512.b do not have complex multiplication.Modular form 8512.2.a.b
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
