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SageMath
E = EllipticCurve("dn1")
E.isogeny_class()
Elliptic curves in class 296208.dn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 296208.dn1 | 296208dn3 | \([0, 0, 0, -289143753195, 59843754773317658]\) | \(505384091400037554067434625/815656731648\) | \(4314704046582253907607552\) | \([2]\) | \(796262400\) | \(4.8823\) | |
| 296208.dn2 | 296208dn4 | \([0, 0, 0, -289140965355, 59844966463925786]\) | \(-505369473241574671219626625/20303219722982711328\) | \(-107401043721425816866346814799872\) | \([2]\) | \(1592524800\) | \(5.2289\) | |
| 296208.dn3 | 296208dn1 | \([0, 0, 0, -3579726315, 81604703078426]\) | \(959024269496848362625/11151660319506432\) | \(58990641577209294100384186368\) | \([2]\) | \(265420800\) | \(4.3330\) | \(\Gamma_0(N)\)-optimal |
| 296208.dn4 | 296208dn2 | \([0, 0, 0, -724978155, 208174530349082]\) | \(-7966267523043306625/3534510366354604032\) | \(-18697039561709266546713604128768\) | \([2]\) | \(530841600\) | \(4.6796\) |
Rank
sage: E.rank()
The elliptic curves in class 296208.dn have rank \(0\).
Complex multiplication
The elliptic curves in class 296208.dn do not have complex multiplication.Modular form 296208.2.a.dn
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
