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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 222180g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
222180.v2 | 222180g1 | \([0, 1, 0, 9468395, 7378393175]\) | \(2477112820760576/2053567248075\) | \(-77824423216656937900800\) | \([]\) | \(20528640\) | \(3.0801\) | \(\Gamma_0(N)\)-optimal |
222180.v1 | 222180g2 | \([0, 1, 0, -200777365, 1110522127463]\) | \(-23618971583050153984/391556092921875\) | \(-14838874703118431532000000\) | \([]\) | \(61585920\) | \(3.6294\) |
Rank
sage: E.rank()
The elliptic curves in class 222180g have rank \(1\).
Complex multiplication
The elliptic curves in class 222180g do not have complex multiplication.Modular form 222180.2.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 Cremona 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 Cremona labels.