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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 240318be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 240318.be3 | 240318be1 | \([1, -1, 0, -70758, -7226712]\) | \(11134383337/316\) | \(1111923028476\) | \([]\) | \(820800\) | \(1.4130\) | \(\Gamma_0(N)\)-optimal |
| 240318.be2 | 240318be2 | \([1, -1, 0, -123993, 5070573]\) | \(59914169497/31554496\) | \(111032185931499456\) | \([]\) | \(2462400\) | \(1.9623\) | |
| 240318.be1 | 240318be3 | \([1, -1, 0, -7934328, 8604249408]\) | \(15698803397448457/20709376\) | \(72870987594203136\) | \([]\) | \(7387200\) | \(2.5116\) |
Rank
sage: E.rank()
The elliptic curves in class 240318be have rank \(1\).
Complex multiplication
The elliptic curves in class 240318be do not have complex multiplication.Modular form 240318.2.a.be
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
