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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 7488.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7488.g1 | 7488t3 | \([0, 0, 0, -264684, 52413104]\) | \(-10730978619193/6656\) | \(-1271981408256\) | \([]\) | \(34560\) | \(1.6434\) | |
| 7488.g2 | 7488t2 | \([0, 0, 0, -2604, 101936]\) | \(-10218313/17576\) | \(-3358825906176\) | \([]\) | \(11520\) | \(1.0941\) | |
| 7488.g3 | 7488t1 | \([0, 0, 0, 276, -2896]\) | \(12167/26\) | \(-4968677376\) | \([]\) | \(3840\) | \(0.54480\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7488.g have rank \(0\).
Complex multiplication
The elliptic curves in class 7488.g do not have complex multiplication.Modular form 7488.2.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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
