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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 24843g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
24843.a2 | 24843g1 | \([0, -1, 1, -394, -3144]\) | \(-28672/3\) | \(-709540923\) | \([]\) | \(14040\) | \(0.43739\) | \(\Gamma_0(N)\)-optimal |
24843.a1 | 24843g2 | \([0, -1, 1, -154184, 23372936]\) | \(-1713910976512/1594323\) | \(-377079137660043\) | \([]\) | \(182520\) | \(1.7199\) |
Rank
sage: E.rank()
The elliptic curves in class 24843g have rank \(0\).
Complex multiplication
The elliptic curves in class 24843g do not have complex multiplication.Modular form 24843.2.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.
\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.