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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 8400.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8400.u1 | 8400m1 | \([0, -1, 0, -15428, 742752]\) | \(12692020761488/9261\) | \(296352000\) | \([2]\) | \(9216\) | \(0.93668\) | \(\Gamma_0(N)\)-optimal |
8400.u2 | 8400m2 | \([0, -1, 0, -15328, 752752]\) | \(-3111705953492/85766121\) | \(-10978063488000\) | \([2]\) | \(18432\) | \(1.2833\) |
Rank
sage: E.rank()
The elliptic curves in class 8400.u have rank \(1\).
Complex multiplication
The elliptic curves in class 8400.u do not have complex multiplication.Modular form 8400.2.a.u
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.