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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 480240.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
480240.o1 | 480240o1 | \([0, 0, 0, -351843, 80326642]\) | \(174223500965896428/5513171875\) | \(152428176000000\) | \([2]\) | \(2101248\) | \(1.8171\) | \(\Gamma_0(N)\)-optimal |
480240.o2 | 480240o2 | \([0, 0, 0, -336843, 87487642]\) | \(-76438573834538214/15562272831125\) | \(-860531438469888000\) | \([2]\) | \(4202496\) | \(2.1637\) |
Rank
sage: E.rank()
The elliptic curves in class 480240.o have rank \(1\).
Complex multiplication
The elliptic curves in class 480240.o do not have complex multiplication.Modular form 480240.2.a.o
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.