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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 215600.v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 215600.v1 | 215600o1 | \([0, 1, 0, -872608, 1112889588]\) | \(-243979633825/1636214272\) | \(-492797370589511680000\) | \([]\) | \(5971968\) | \(2.6539\) | \(\Gamma_0(N)\)-optimal |
| 215600.v2 | 215600o2 | \([0, 1, 0, 7751392, -27929292812]\) | \(171015136702175/1218033273688\) | \(-366849015337265950720000\) | \([]\) | \(17915904\) | \(3.2032\) |
Rank
sage: E.rank()
The elliptic curves in class 215600.v have rank \(0\).
Complex multiplication
The elliptic curves in class 215600.v do not have complex multiplication.Modular form 215600.2.a.v
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
