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SageMath
E = EllipticCurve("rn1")
E.isogeny_class()
Elliptic curves in class 369600.rn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 369600.rn1 | 369600rn2 | \([0, 1, 0, -90656432833, 2818545808546463]\) | \(160934676078320454012702173/86430430219822569086976\) | \(44252380272549155372531712000000000\) | \([2]\) | \(3220439040\) | \(5.3391\) | |
| 369600.rn2 | 369600rn1 | \([0, 1, 0, 21737807167, 345535345826463]\) | \(2218712073897830722499107/1384711926834951880704\) | \(-708972506539495362920448000000000\) | \([2]\) | \(1610219520\) | \(4.9925\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 369600.rn have rank \(0\).
Complex multiplication
The elliptic curves in class 369600.rn do not have complex multiplication.Modular form 369600.2.a.rn
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 LMFDB 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 LMFDB labels.
