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SageMath
E = EllipticCurve("dv1")
E.isogeny_class()
Elliptic curves in class 85680.dv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 85680.dv1 | 85680fe4 | \([0, 0, 0, -8812947, -10070008814]\) | \(25351269426118370449/27551475\) | \(82268263526400\) | \([2]\) | \(1572864\) | \(2.3888\) | |
| 85680.dv2 | 85680fe3 | \([0, 0, 0, -687027, -73626446]\) | \(12010404962647729/6166198828125\) | \(18412171041600000000\) | \([4]\) | \(1572864\) | \(2.3888\) | |
| 85680.dv3 | 85680fe2 | \([0, 0, 0, -550947, -157261214]\) | \(6193921595708449/6452105625\) | \(19265884162560000\) | \([2, 2]\) | \(786432\) | \(2.0423\) | |
| 85680.dv4 | 85680fe1 | \([0, 0, 0, -26067, -3681326]\) | \(-656008386769/1581036975\) | \(-4720951110758400\) | \([2]\) | \(393216\) | \(1.6957\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 85680.dv have rank \(1\).
Complex multiplication
The elliptic curves in class 85680.dv do not have complex multiplication.Modular form 85680.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
