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SageMath
E = EllipticCurve("el1")
E.isogeny_class()
Elliptic curves in class 39600.el
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
39600.el1 | 39600fc2 | \([0, 0, 0, -3250875, 2257686250]\) | \(-3257444411545/2737152\) | \(-3192614092800000000\) | \([]\) | \(1152000\) | \(2.4783\) | |
39600.el2 | 39600fc1 | \([0, 0, 0, 35925, -1216550]\) | \(2747555975/1932612\) | \(-3606717818880000\) | \([]\) | \(230400\) | \(1.6736\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 39600.el have rank \(1\).
Complex multiplication
The elliptic curves in class 39600.el do not have complex multiplication.Modular form 39600.2.a.el
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.