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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 38962f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
38962.c3 | 38962f1 | \([1, 0, 1, -3695101, -2997790248]\) | \(-3149534523783390625/368345236897792\) | \(-652546056223889293312\) | \([2]\) | \(1658880\) | \(2.7300\) | \(\Gamma_0(N)\)-optimal |
38962.c2 | 38962f2 | \([1, 0, 1, -60690941, -181987526184]\) | \(13955300880533969118625/162273186639872\) | \(287476848796918280192\) | \([2]\) | \(3317760\) | \(3.0766\) | |
38962.c4 | 38962f3 | \([1, 0, 1, 23408899, 5184148440]\) | \(800775157152056609375/469960256734490368\) | \(-832563262380810490824448\) | \([2]\) | \(4976640\) | \(3.2793\) | |
38962.c1 | 38962f4 | \([1, 0, 1, -94367661, 41600660792]\) | \(52461072723569038782625/29937242318698495088\) | \(53035650939355824656592368\) | \([2]\) | \(9953280\) | \(3.6259\) |
Rank
sage: E.rank()
The elliptic curves in class 38962f have rank \(0\).
Complex multiplication
The elliptic curves in class 38962f do not have complex multiplication.Modular form 38962.2.a.f
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.