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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 222180n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 222180.p2 | 222180n1 | \([0, 1, 0, 52724, -4687900]\) | \(808496/945\) | \(-18944993559179520\) | \([3]\) | \(1669248\) | \(1.8097\) | \(\Gamma_0(N)\)-optimal |
| 222180.p1 | 222180n2 | \([0, 1, 0, -1407316, -647689516]\) | \(-15375747664/128625\) | \(-2578624123332768000\) | \([]\) | \(5007744\) | \(2.3590\) |
Rank
sage: E.rank()
The elliptic curves in class 222180n have rank \(1\).
Complex multiplication
The elliptic curves in class 222180n do not have complex multiplication.Modular form 222180.2.a.n
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
