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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 37485bl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 37485.t2 | 37485bl1 | \([1, -1, 1, -1112, -74014]\) | \(-1771561/26775\) | \(-2296387889775\) | \([2]\) | \(49152\) | \(1.0533\) | \(\Gamma_0(N)\)-optimal |
| 37485.t1 | 37485bl2 | \([1, -1, 1, -34187, -2415724]\) | \(51520374361/212415\) | \(18218010592215\) | \([2]\) | \(98304\) | \(1.3998\) |
Rank
sage: E.rank()
The elliptic curves in class 37485bl have rank \(0\).
Complex multiplication
The elliptic curves in class 37485bl do not have complex multiplication.Modular form 37485.2.a.bl
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
