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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 364140.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 364140.h1 | 364140h4 | \([0, 0, 0, -1100223, -178017642]\) | \(1210991472/588245\) | \(71545616530554781440\) | \([2]\) | \(7962624\) | \(2.5032\) | |
| 364140.h2 | 364140h3 | \([0, 0, 0, -905148, -331229547]\) | \(10788913152/8575\) | \(65183688530024400\) | \([2]\) | \(3981312\) | \(2.1567\) | |
| 364140.h3 | 364140h2 | \([0, 0, 0, -580023, 170019278]\) | \(129348709488/6125\) | \(1021888121184000\) | \([2]\) | \(2654208\) | \(1.9539\) | |
| 364140.h4 | 364140h1 | \([0, 0, 0, -38148, 2363153]\) | \(588791808/109375\) | \(1140500135250000\) | \([2]\) | \(1327104\) | \(1.6074\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 364140.h have rank \(2\).
Complex multiplication
The elliptic curves in class 364140.h do not have complex multiplication.Modular form 364140.2.a.h
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.
