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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 430950bd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
430950.bd2 | 430950bd1 | \([1, 1, 0, -48675, 4112685]\) | \(105695235625/14688\) | \(1772404264800\) | \([]\) | \(1658880\) | \(1.3674\) | \(\Gamma_0(N)\)-optimal |
430950.bd1 | 430950bd2 | \([1, 1, 0, -112050, -8620620]\) | \(1289333385625/482967552\) | \(58279803167539200\) | \([]\) | \(4976640\) | \(1.9167\) |
Rank
sage: E.rank()
The elliptic curves in class 430950bd have rank \(0\).
Complex multiplication
The elliptic curves in class 430950bd do not have complex multiplication.Modular form 430950.2.a.bd
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.