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SageMath
E = EllipticCurve("dv1")
E.isogeny_class()
Elliptic curves in class 79350dv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
79350.dr4 | 79350dv1 | \([1, 0, 0, -1598, 33312]\) | \(-24389/12\) | \(-222053833500\) | \([2]\) | \(98560\) | \(0.88248\) | \(\Gamma_0(N)\)-optimal |
79350.dr2 | 79350dv2 | \([1, 0, 0, -28048, 1805462]\) | \(131872229/18\) | \(333080750250\) | \([2]\) | \(197120\) | \(1.2290\) | |
79350.dr3 | 79350dv3 | \([1, 0, 0, -14823, -3339063]\) | \(-19465109/248832\) | \(-4604508291456000\) | \([2]\) | \(492800\) | \(1.6872\) | |
79350.dr1 | 79350dv4 | \([1, 0, 0, -438023, -111255063]\) | \(502270291349/1889568\) | \(34965484838244000\) | \([2]\) | \(985600\) | \(2.0338\) |
Rank
sage: E.rank()
The elliptic curves in class 79350dv have rank \(1\).
Complex multiplication
The elliptic curves in class 79350dv do not have complex multiplication.Modular form 79350.2.a.dv
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.