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SageMath
E = EllipticCurve("cv1")
E.isogeny_class()
Elliptic curves in class 115920cv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 115920.u2 | 115920cv1 | \([0, 0, 0, -791643, -269361398]\) | \(18374873741826841/136564270080\) | \(407778725430558720\) | \([2]\) | \(1228800\) | \(2.2097\) | \(\Gamma_0(N)\)-optimal |
| 115920.u1 | 115920cv2 | \([0, 0, 0, -1321563, 136451338]\) | \(85486955243540761/46777901234400\) | \(139678064639498649600\) | \([2]\) | \(2457600\) | \(2.5562\) |
Rank
sage: E.rank()
The elliptic curves in class 115920cv have rank \(1\).
Complex multiplication
The elliptic curves in class 115920cv do not have complex multiplication.Modular form 115920.2.a.cv
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.
