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SageMath
E = EllipticCurve("dm1")
E.isogeny_class()
Elliptic curves in class 115920.dm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 115920.dm1 | 115920ck1 | \([0, 0, 0, -183627, -29710854]\) | \(8493409990827/185150000\) | \(14927083315200000\) | \([2]\) | \(737280\) | \(1.8918\) | \(\Gamma_0(N)\)-optimal |
| 115920.dm2 | 115920ck2 | \([0, 0, 0, 15093, -90638406]\) | \(4716275733/44023437500\) | \(-3549238560000000000\) | \([2]\) | \(1474560\) | \(2.2383\) |
Rank
sage: E.rank()
The elliptic curves in class 115920.dm have rank \(1\).
Complex multiplication
The elliptic curves in class 115920.dm do not have complex multiplication.Modular form 115920.2.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 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.
