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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 311696.e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 311696.e1 | 311696e2 | \([0, 1, 0, -16417364, 25598259256]\) | \(1436203562785124669552/13712209\) | \(4672243245824\) | \([2]\) | \(7096320\) | \(2.4651\) | |
| 311696.e2 | 311696e1 | \([0, 1, 0, -1026109, 399696570]\) | \(5610564864985137152/548176896967\) | \(11673975197809232\) | \([2]\) | \(3548160\) | \(2.1185\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 311696.e have rank \(1\).
Complex multiplication
The elliptic curves in class 311696.e do not have complex multiplication.Modular form 311696.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
