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SageMath
E = EllipticCurve("cz1")
E.isogeny_class()
Elliptic curves in class 66880cz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 66880.w2 | 66880cz1 | \([0, 1, 0, -385, 2175]\) | \(24137569/5225\) | \(1369702400\) | \([2]\) | \(32768\) | \(0.46710\) | \(\Gamma_0(N)\)-optimal |
| 66880.w1 | 66880cz2 | \([0, 1, 0, -1985, -32705]\) | \(3301293169/218405\) | \(57253560320\) | \([2]\) | \(65536\) | \(0.81368\) |
Rank
sage: E.rank()
The elliptic curves in class 66880cz have rank \(1\).
Complex multiplication
The elliptic curves in class 66880cz do not have complex multiplication.Modular form 66880.2.a.cz
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.
