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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 380880.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
380880.u1 | 380880u2 | \([0, 0, 0, -712563, 224043138]\) | \(9776035692/359375\) | \(1470884593104000000\) | \([2]\) | \(4866048\) | \(2.2554\) | |
380880.u2 | 380880u1 | \([0, 0, 0, 17457, 12483342]\) | \(574992/66125\) | \(-67660691282784000\) | \([2]\) | \(2433024\) | \(1.9088\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 380880.u have rank \(2\).
Complex multiplication
The elliptic curves in class 380880.u do not have complex multiplication.Modular form 380880.2.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.