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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 235200.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
235200.g1 | 235200g1 | \([0, -1, 0, -56513, 5024097]\) | \(5177717/189\) | \(728618139648000\) | \([2]\) | \(1179648\) | \(1.6215\) | \(\Gamma_0(N)\)-optimal |
235200.g2 | 235200g2 | \([0, -1, 0, 21887, 17803297]\) | \(300763/35721\) | \(-137708828393472000\) | \([2]\) | \(2359296\) | \(1.9680\) |
Rank
sage: E.rank()
The elliptic curves in class 235200.g have rank \(2\).
Complex multiplication
The elliptic curves in class 235200.g do not have complex multiplication.Modular form 235200.2.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.