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SageMath
E = EllipticCurve("dm1")
E.isogeny_class()
Elliptic curves in class 466752.dm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
466752.dm1 | 466752dm1 | \([0, 1, 0, -193313, -29820609]\) | \(3047678972871625/304559880768\) | \(79838545384046592\) | \([2]\) | \(4128768\) | \(1.9796\) | \(\Gamma_0(N)\)-optimal |
466752.dm2 | 466752dm2 | \([0, 1, 0, 239327, -143951041]\) | \(5783051584712375/37533175779528\) | \(-9839096831548588032\) | \([2]\) | \(8257536\) | \(2.3262\) |
Rank
sage: E.rank()
The elliptic curves in class 466752.dm have rank \(0\).
Complex multiplication
The elliptic curves in class 466752.dm do not have complex multiplication.Modular form 466752.2.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.