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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 97020.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 97020.c1 | 97020bn2 | \([0, 0, 0, -337008, -75302332]\) | \(462893166690304/4125\) | \(37721376000\) | \([]\) | \(373248\) | \(1.6126\) | |
| 97020.c2 | 97020bn1 | \([0, 0, 0, -4368, -92428]\) | \(1007878144/179685\) | \(1643143138560\) | \([]\) | \(124416\) | \(1.0633\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 97020.c have rank \(0\).
Complex multiplication
The elliptic curves in class 97020.c do not have complex multiplication.Modular form 97020.2.a.c
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.
