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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 7245.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7245.m1 | 7245k1 | \([1, -1, 0, -2070, 31671]\) | \(1345938541921/203765625\) | \(148545140625\) | \([2]\) | \(6144\) | \(0.86766\) | \(\Gamma_0(N)\)-optimal |
| 7245.m2 | 7245k2 | \([1, -1, 0, 3555, 170046]\) | \(6814692748079/21258460125\) | \(-15497417431125\) | \([2]\) | \(12288\) | \(1.2142\) |
Rank
sage: E.rank()
The elliptic curves in class 7245.m have rank \(1\).
Complex multiplication
The elliptic curves in class 7245.m do not have complex multiplication.Modular form 7245.2.a.m
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.
