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SageMath
E = EllipticCurve("dh1")
E.isogeny_class()
Elliptic curves in class 301392.dh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
301392.dh1 | 301392dh1 | \([0, 0, 0, -6290976, 6073305968]\) | \(-9221261135586623488/121324931\) | \(-362274302767104\) | \([]\) | \(7464960\) | \(2.3520\) | \(\Gamma_0(N)\)-optimal |
301392.dh2 | 301392dh2 | \([0, 0, 0, -5935296, 6790304432]\) | \(-7743965038771437568/2189290237869371\) | \(-6537185621634135896064\) | \([]\) | \(22394880\) | \(2.9013\) |
Rank
sage: E.rank()
The elliptic curves in class 301392.dh have rank \(0\).
Complex multiplication
The elliptic curves in class 301392.dh do not have complex multiplication.Modular form 301392.2.a.dh
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.