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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 7056.w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7056.w1 | 7056bk2 | \([0, 0, 0, -995043, -396371486]\) | \(-6329617441/279936\) | \(-4818707323144372224\) | \([]\) | \(112896\) | \(2.3499\) | |
| 7056.w2 | 7056bk1 | \([0, 0, 0, -7203, 542626]\) | \(-2401/6\) | \(-103281621295104\) | \([]\) | \(16128\) | \(1.3769\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7056.w have rank \(1\).
Complex multiplication
The elliptic curves in class 7056.w do not have complex multiplication.Modular form 7056.2.a.w
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.
