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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 756.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
756.e1 | 756d2 | \([0, 0, 0, -2376, -44172]\) | \(32710656/343\) | \(15554923776\) | \([]\) | \(648\) | \(0.77219\) | |
756.e2 | 756d1 | \([0, 0, 0, -216, 1188]\) | \(221184/7\) | \(35271936\) | \([3]\) | \(216\) | \(0.22289\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 756.e have rank \(0\).
Complex multiplication
The elliptic curves in class 756.e do not have complex multiplication.Modular form 756.2.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.