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SageMath
E = EllipticCurve("dm1")
E.isogeny_class()
Elliptic curves in class 350658dm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 350658.dm2 | 350658dm1 | \([1, -1, 1, -172085, 39837845]\) | \(-52802213121625/33540304392\) | \(-357985361923785288\) | \([]\) | \(4810752\) | \(2.0697\) | \(\Gamma_0(N)\)-optimal |
| 350658.dm1 | 350658dm2 | \([1, -1, 1, -15608660, 23739302711]\) | \(-39402364010111991625/3532128768\) | \(-37699431126077952\) | \([3]\) | \(14432256\) | \(2.6190\) |
Rank
sage: E.rank()
The elliptic curves in class 350658dm have rank \(0\).
Complex multiplication
The elliptic curves in class 350658dm do not have complex multiplication.Modular form 350658.2.a.dm
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.
