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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 235950.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 235950.h1 | 235950h4 | \([1, 1, 0, -197155950, 1065330520500]\) | \(30618029936661765625/3678951124992\) | \(101835723967843008000000\) | \([2]\) | \(59719680\) | \(3.4395\) | |
| 235950.h2 | 235950h3 | \([1, 1, 0, -11299950, 19518808500]\) | \(-5764706497797625/2612665516032\) | \(-72320255222611968000000\) | \([2]\) | \(29859840\) | \(3.0929\) | |
| 235950.h3 | 235950h2 | \([1, 1, 0, -5446575, -2789764875]\) | \(645532578015625/252306960048\) | \(6984018288274920750000\) | \([2]\) | \(19906560\) | \(2.8902\) | |
| 235950.h4 | 235950h1 | \([1, 1, 0, 1087425, -313378875]\) | \(5137417856375/4510142208\) | \(-124843625627292000000\) | \([2]\) | \(9953280\) | \(2.5436\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 235950.h have rank \(1\).
Complex multiplication
The elliptic curves in class 235950.h do not have complex multiplication.Modular form 235950.2.a.h
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
