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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 302330.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
302330.c1 | 302330c2 | \([1, 0, 1, -13809059, -19752821154]\) | \(-50516307977225837929/1293942784000\) | \(-7459322655145984000\) | \([]\) | \(23587200\) | \(2.7285\) | |
302330.c2 | 302330c1 | \([1, 0, 1, -53044, -63519438]\) | \(-2863099371769/300652944640\) | \(-1733204395913616640\) | \([3]\) | \(7862400\) | \(2.1792\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 302330.c have rank \(0\).
Complex multiplication
The elliptic curves in class 302330.c do not have complex multiplication.Modular form 302330.2.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.