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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 13520a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 13520.l3 | 13520a1 | \([0, 0, 0, -338, -2197]\) | \(55296/5\) | \(386144720\) | \([2]\) | \(4608\) | \(0.38711\) | \(\Gamma_0(N)\)-optimal |
| 13520.l2 | 13520a2 | \([0, 0, 0, -1183, 13182]\) | \(148176/25\) | \(30891577600\) | \([2, 2]\) | \(9216\) | \(0.73369\) | |
| 13520.l1 | 13520a3 | \([0, 0, 0, -18083, 935922]\) | \(132304644/5\) | \(24713262080\) | \([2]\) | \(18432\) | \(1.0803\) | |
| 13520.l4 | 13520a4 | \([0, 0, 0, 2197, 74698]\) | \(237276/625\) | \(-3089157760000\) | \([2]\) | \(18432\) | \(1.0803\) |
Rank
sage: E.rank()
The elliptic curves in class 13520a have rank \(1\).
Complex multiplication
The elliptic curves in class 13520a do not have complex multiplication.Modular form 13520.2.a.a
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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
