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SageMath
E = EllipticCurve("dp1")
E.isogeny_class()
Elliptic curves in class 308550.dp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
308550.dp1 | 308550dp2 | \([1, 0, 1, -2175303276, 38903128502698]\) | \(41125104693338423360329/179205840000000000\) | \(4960532454941250000000000000\) | \([2]\) | \(287539200\) | \(4.1673\) | |
308550.dp2 | 308550dp1 | \([1, 0, 1, -68935276, 1207566774698]\) | \(-1308796492121439049/22000592486400000\) | \(-608990494153113600000000000\) | \([2]\) | \(143769600\) | \(3.8207\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 308550.dp have rank \(0\).
Complex multiplication
The elliptic curves in class 308550.dp do not have complex multiplication.Modular form 308550.2.a.dp
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.