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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 112014.e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 112014.e1 | 112014l2 | \([1, -1, 0, -9861247755, -376914692187923]\) | \(1236526859255318155975783969/38367061931916216\) | \(3290594076067219943318136\) | \([]\) | \(78236928\) | \(4.2087\) | |
| 112014.e2 | 112014l1 | \([1, -1, 0, -44958195, 114943838197]\) | \(117174888570509216929/1273887851544576\) | \(109256419616002142109696\) | \([]\) | \(11176704\) | \(3.2358\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 112014.e have rank \(0\).
Complex multiplication
The elliptic curves in class 112014.e do not have complex multiplication.Modular form 112014.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
