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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 63870p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
63870.o2 | 63870p1 | \([1, 0, 0, -35874060, 82698195600]\) | \(5105817686570071165887579841/97645976616960000000\) | \(97645976616960000000\) | \([7]\) | \(4346496\) | \(2.9589\) | \(\Gamma_0(N)\)-optimal |
63870.o1 | 63870p2 | \([1, 0, 0, -1345660860, -18997123438560]\) | \(269482504024993568727413630831041/47581800502396103180402160\) | \(47581800502396103180402160\) | \([]\) | \(30425472\) | \(3.9319\) |
Rank
sage: E.rank()
The elliptic curves in class 63870p have rank \(1\).
Complex multiplication
The elliptic curves in class 63870p do not have complex multiplication.Modular form 63870.2.a.p
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.