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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 234416.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
234416.g1 | 234416g2 | \([0, 1, 0, -141248, -20566988]\) | \(-1552807715412625/7697866228\) | \(-1544992543424512\) | \([]\) | \(1306368\) | \(1.7623\) | |
234416.g2 | 234416g1 | \([0, 1, 0, 4352, -148044]\) | \(45408227375/74381632\) | \(-14928691068928\) | \([]\) | \(435456\) | \(1.2130\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 234416.g have rank \(0\).
Complex multiplication
The elliptic curves in class 234416.g do not have complex multiplication.Modular form 234416.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.