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SageMath
E = EllipticCurve("db1")
E.isogeny_class()
Elliptic curves in class 303450.db
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
303450.db1 | 303450db2 | \([1, 0, 1, -1849751, -990728872]\) | \(-1159924308480625/31212514998\) | \(-18834855860693996550\) | \([]\) | \(8957952\) | \(2.4804\) | |
303450.db2 | 303450db1 | \([1, 0, 1, 100999, -5522092]\) | \(188819819375/131167512\) | \(-79151621786458200\) | \([]\) | \(2985984\) | \(1.9311\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 303450.db have rank \(1\).
Complex multiplication
The elliptic curves in class 303450.db do not have complex multiplication.Modular form 303450.2.a.db
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.