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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 468468.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
468468.e1 | 468468e2 | \([0, 0, 0, -104949, -13584051]\) | \(-84098304/3773\) | \(-5735327130829296\) | \([]\) | \(3545856\) | \(1.7883\) | |
468468.e2 | 468468e1 | \([0, 0, 0, 6591, -50531]\) | \(15185664/9317\) | \(-19427635923696\) | \([]\) | \(1181952\) | \(1.2390\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 468468.e have rank \(0\).
Complex multiplication
The elliptic curves in class 468468.e do not have complex multiplication.Modular form 468468.2.a.e
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.