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SageMath
E = EllipticCurve("cc1")
E.isogeny_class()
Elliptic curves in class 58950cc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 58950.ck1 | 58950cc1 | \([1, -1, 1, -15980, 777647]\) | \(39616946929/226368\) | \(2578473000000\) | \([2]\) | \(184320\) | \(1.2230\) | \(\Gamma_0(N)\)-optimal |
| 58950.ck2 | 58950cc2 | \([1, -1, 1, -6980, 1641647]\) | \(-3301293169/100082952\) | \(-1140007375125000\) | \([2]\) | \(368640\) | \(1.5696\) |
Rank
sage: E.rank()
The elliptic curves in class 58950cc have rank \(0\).
Complex multiplication
The elliptic curves in class 58950cc do not have complex multiplication.Modular form 58950.2.a.cc
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.
