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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 344760.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
344760.g1 | 344760g2 | \([0, -1, 0, -7297476, -7584892524]\) | \(34780972302198736/1711783125\) | \(2115187249612320000\) | \([2]\) | \(10321920\) | \(2.5881\) | |
344760.g2 | 344760g1 | \([0, -1, 0, -431851, -131570024]\) | \(-115331093579776/30301171875\) | \(-2340127505868750000\) | \([2]\) | \(5160960\) | \(2.2416\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 344760.g have rank \(0\).
Complex multiplication
The elliptic curves in class 344760.g do not have complex multiplication.Modular form 344760.2.a.g
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.