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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 12480.z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 12480.z1 | 12480ch2 | \([0, -1, 0, -2945, 56097]\) | \(10779215329/1232010\) | \(322964029440\) | \([2]\) | \(18432\) | \(0.94068\) | |
| 12480.z2 | 12480ch1 | \([0, -1, 0, 255, 4257]\) | \(6967871/35100\) | \(-9201254400\) | \([2]\) | \(9216\) | \(0.59410\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 12480.z have rank \(0\).
Complex multiplication
The elliptic curves in class 12480.z do not have complex multiplication.Modular form 12480.2.a.z
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.
