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SageMath
E = EllipticCurve("sr1")
E.isogeny_class()
Elliptic curves in class 1270080.sr
sage: E.isogeny_class().curves
| LMFDB label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height |
|---|---|---|---|---|---|---|
| 1270080.sr1 | \([0, 0, 0, -6355692, 6193904976]\) | \(-15590912409/78125\) | \(-142275702804480000000\) | \([]\) | \(42577920\) | \(2.7143\) |
| 1270080.sr2 | \([0, 0, 0, -5292, -4593456]\) | \(-9/5\) | \(-9105644979486720\) | \([]\) | \(6082560\) | \(1.7414\) |
Rank
sage: E.rank()
The elliptic curves in class 1270080.sr have rank \(1\).
Complex multiplication
The elliptic curves in class 1270080.sr do not have complex multiplication.Modular form 1270080.2.a.sr
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.
