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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 35301.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
35301.c1 | 35301e6 | \([1, 1, 1, -1317939, -582908538]\) | \(53297461115137/147\) | \(698265323427\) | \([2]\) | \(281600\) | \(1.9310\) | |
35301.c2 | 35301e4 | \([1, 1, 1, -82404, -9126084]\) | \(13027640977/21609\) | \(102645002543769\) | \([2, 2]\) | \(140800\) | \(1.5844\) | |
35301.c3 | 35301e3 | \([1, 1, 1, -65594, 6399632]\) | \(6570725617/45927\) | \(218158037476407\) | \([2]\) | \(140800\) | \(1.5844\) | |
35301.c4 | 35301e5 | \([1, 1, 1, -57189, -14784330]\) | \(-4354703137/17294403\) | \(-82150217035863123\) | \([2]\) | \(281600\) | \(1.9310\) | |
35301.c5 | 35301e2 | \([1, 1, 1, -6759, -48684]\) | \(7189057/3969\) | \(18853163732529\) | \([2, 2]\) | \(70400\) | \(1.2378\) | |
35301.c6 | 35301e1 | \([1, 1, 1, 1646, -4978]\) | \(103823/63\) | \(-299256567183\) | \([2]\) | \(35200\) | \(0.89127\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 35301.c have rank \(0\).
Complex multiplication
The elliptic curves in class 35301.c do not have complex multiplication.Modular form 35301.2.a.c
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 8 & 4 & 4 & 8 \\ 2 & 1 & 4 & 2 & 2 & 4 \\ 8 & 4 & 1 & 8 & 2 & 4 \\ 4 & 2 & 8 & 1 & 4 & 8 \\ 4 & 2 & 2 & 4 & 1 & 2 \\ 8 & 4 & 4 & 8 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.