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SageMath
E = EllipticCurve("ms1")
E.isogeny_class()
Elliptic curves in class 327600ms
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 327600.ms3 | 327600ms1 | \([0, 0, 0, 48525, 39123250]\) | \(270840023/14329224\) | \(-668544274944000000\) | \([]\) | \(4478976\) | \(2.1000\) | \(\Gamma_0(N)\)-optimal |
| 327600.ms2 | 327600ms2 | \([0, 0, 0, -437475, -1066526750]\) | \(-198461344537/10417365504\) | \(-486032604954624000000\) | \([]\) | \(13436928\) | \(2.6493\) | |
| 327600.ms1 | 327600ms3 | \([0, 0, 0, -93803475, -349690256750]\) | \(-1956469094246217097/36641439744\) | \(-1709543012696064000000\) | \([]\) | \(40310784\) | \(3.1986\) |
Rank
sage: E.rank()
The elliptic curves in class 327600ms have rank \(0\).
Complex multiplication
The elliptic curves in class 327600ms do not have complex multiplication.Modular form 327600.2.a.ms
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
