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SageMath
E = EllipticCurve("jr1")
E.isogeny_class()
Elliptic curves in class 388080jr
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
388080.jr1 | 388080jr1 | \([0, 0, 0, -53067, -4629814]\) | \(188183524/3465\) | \(304311919887360\) | \([2]\) | \(1769472\) | \(1.5737\) | \(\Gamma_0(N)\)-optimal |
388080.jr2 | 388080jr2 | \([0, 0, 0, -147, -13446286]\) | \(-2/444675\) | \(-78106726104422400\) | \([2]\) | \(3538944\) | \(1.9203\) |
Rank
sage: E.rank()
The elliptic curves in class 388080jr have rank \(0\).
Complex multiplication
The elliptic curves in class 388080jr do not have complex multiplication.Modular form 388080.2.a.jr
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.