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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 7350.bc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7350.bc1 | 7350bh2 | \([1, 0, 1, -9270826, 9492495548]\) | \(1118063669939/153055008\) | \(12063128207448937500000\) | \([2]\) | \(627200\) | \(2.9639\) | |
7350.bc2 | 7350bh1 | \([1, 0, 1, -2410826, -1291424452]\) | \(19661138099/2239488\) | \(176506677018000000000\) | \([2]\) | \(313600\) | \(2.6174\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7350.bc have rank \(0\).
Complex multiplication
The elliptic curves in class 7350.bc do not have complex multiplication.Modular form 7350.2.a.bc
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.