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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 331298.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
331298.e1 | 331298e2 | \([1, 0, 1, -71217, 7507652]\) | \(-128667913/4096\) | \(-1271615059922944\) | \([]\) | \(2410560\) | \(1.6743\) | |
331298.e2 | 331298e1 | \([1, 0, 1, 4078, 38388]\) | \(24167/16\) | \(-4967246327824\) | \([]\) | \(803520\) | \(1.1249\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 331298.e have rank \(0\).
Complex multiplication
The elliptic curves in class 331298.e do not have complex multiplication.Modular form 331298.2.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.