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SageMath
E = EllipticCurve("dm1")
E.isogeny_class()
Elliptic curves in class 364650.dm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
364650.dm1 | 364650dm2 | \([1, 1, 1, -24818938, 25303057031]\) | \(108206480032729847921881/44903533467320985600\) | \(701617710426890400000000\) | \([2]\) | \(66232320\) | \(3.2729\) | |
364650.dm2 | 364650dm1 | \([1, 1, 1, 5133062, 2898961031]\) | \(957267271071458067239/785984496347381760\) | \(-12281007755427840000000\) | \([2]\) | \(33116160\) | \(2.9263\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 364650.dm have rank \(1\).
Complex multiplication
The elliptic curves in class 364650.dm do not have complex multiplication.Modular form 364650.2.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.