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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 32340c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
32340.a2 | 32340c1 | \([0, -1, 0, 474, 400401]\) | \(14990845184/88418496375\) | \(-69320101158000\) | \([]\) | \(93312\) | \(1.3347\) | \(\Gamma_0(N)\)-optimal |
32340.a1 | 32340c2 | \([0, -1, 0, -396426, 96212061]\) | \(-8788102954619113216/954968814855\) | \(-748695550846320\) | \([]\) | \(279936\) | \(1.8840\) |
Rank
sage: E.rank()
The elliptic curves in class 32340c have rank \(1\).
Complex multiplication
The elliptic curves in class 32340c do not have complex multiplication.Modular form 32340.2.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 Cremona 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 Cremona labels.