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SageMath
E = EllipticCurve("dm1")
E.isogeny_class()
Elliptic curves in class 129360dm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
129360.bb2 | 129360dm1 | \([0, -1, 0, -23781, 1182105]\) | \(1007878144/179685\) | \(265177156527360\) | \([]\) | \(435456\) | \(1.4869\) | \(\Gamma_0(N)\)-optimal |
129360.bb1 | 129360dm2 | \([0, -1, 0, -1834821, 957230121]\) | \(462893166690304/4125\) | \(6087629856000\) | \([]\) | \(1306368\) | \(2.0362\) |
Rank
sage: E.rank()
The elliptic curves in class 129360dm have rank \(0\).
Complex multiplication
The elliptic curves in class 129360dm do not have complex multiplication.Modular form 129360.2.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.