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SageMath
E = EllipticCurve("ra1")
E.isogeny_class()
Elliptic curves in class 369600ra
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 369600.ra2 | 369600ra1 | \([0, 1, 0, -97833, -18858537]\) | \(-12944768192/11647251\) | \(-93178008000000000\) | \([2]\) | \(2949120\) | \(1.9530\) | \(\Gamma_0(N)\)-optimal |
| 369600.ra1 | 369600ra2 | \([0, 1, 0, -1812833, -939813537]\) | \(10294787169064/3361743\) | \(215151552000000000\) | \([2]\) | \(5898240\) | \(2.2996\) |
Rank
sage: E.rank()
The elliptic curves in class 369600ra have rank \(0\).
Complex multiplication
The elliptic curves in class 369600ra do not have complex multiplication.Modular form 369600.2.a.ra
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.
