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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 63580.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
63580.i1 | 63580g2 | \([0, 1, 0, -4336541, -3477416305]\) | \(-5050365927424/171875\) | \(-306933327404000000\) | \([]\) | \(1586304\) | \(2.4472\) | |
63580.i2 | 63580g1 | \([0, 1, 0, -13101, -11746801]\) | \(-139264/33275\) | \(-59422292185414400\) | \([3]\) | \(528768\) | \(1.8979\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 63580.i have rank \(0\).
Complex multiplication
The elliptic curves in class 63580.i do not have complex multiplication.Modular form 63580.2.a.i
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.