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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 42432l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
42432.m2 | 42432l1 | \([0, -1, 0, -2113, -34751]\) | \(3981876625/232713\) | \(61004316672\) | \([2]\) | \(32768\) | \(0.82304\) | \(\Gamma_0(N)\)-optimal |
42432.m1 | 42432l2 | \([0, -1, 0, -6273, 149121]\) | \(104154702625/24649677\) | \(6461764927488\) | \([2]\) | \(65536\) | \(1.1696\) |
Rank
sage: E.rank()
The elliptic curves in class 42432l have rank \(1\).
Complex multiplication
The elliptic curves in class 42432l do not have complex multiplication.Modular form 42432.2.a.l
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.