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SageMath
E = EllipticCurve("da1")
E.isogeny_class()
Elliptic curves in class 59200.da
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
59200.da1 | 59200bo1 | \([0, -1, 0, -30433, 4893537]\) | \(-19026212425/51868672\) | \(-8498163220480000\) | \([]\) | \(345600\) | \(1.7439\) | \(\Gamma_0(N)\)-optimal |
59200.da2 | 59200bo2 | \([0, -1, 0, 265567, -110960863]\) | \(12642252501575/39728447488\) | \(-6509108836433920000\) | \([]\) | \(1036800\) | \(2.2932\) |
Rank
sage: E.rank()
The elliptic curves in class 59200.da have rank \(0\).
Complex multiplication
The elliptic curves in class 59200.da do not have complex multiplication.Modular form 59200.2.a.da
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.