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SageMath
E = EllipticCurve("ci1")
E.isogeny_class()
Elliptic curves in class 61200ci
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 61200.hc1 | 61200ci1 | \([0, 0, 0, -73290, 7636075]\) | \(29860725364736/3581577\) | \(5221939266000\) | \([2]\) | \(239616\) | \(1.4651\) | \(\Gamma_0(N)\)-optimal |
| 61200.hc2 | 61200ci2 | \([0, 0, 0, -67215, 8954350]\) | \(-1439609866256/651714363\) | \(-15203192660064000\) | \([2]\) | \(479232\) | \(1.8117\) |
Rank
sage: E.rank()
The elliptic curves in class 61200ci have rank \(1\).
Complex multiplication
The elliptic curves in class 61200ci do not have complex multiplication.Modular form 61200.2.a.ci
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.
